AIM 1: Define the concept of statistical inference.

1、 Which one of the following alternatives best describes the primary use of inferential statistics? Inferential statistics are used to:

A) approximate the characteristics of any data set.

B) make forecasts based on large data sets.

C) summarize the important characteristics of a large data set based on statistical characteristics of a smaller sample.

D) make forecasts, estimates or judgments about a large set of data based on statistical characteristics of a smaller sample

The correct answer is D

Inferential statistics are used mainly to make forecasts, estimates or judgements about a large set of data based on statistical characteristics of a smaller set of data.

AIM 2: Define and distinguish between estimator and parameterfficeffice" />

1、Which of the following statements regarding the terms population and sample is least accurate?

A) Observing all members of a population can be expensive or time consuming.

B) A sample includes all members of a specified group.

C) A sample's characteristics are attributed to the population as a whole.

D) A descriptive measure of a sample is called a statistic.

The correct answer is B

A population includes all members of a specified group. A sample is a portion, or subset of the population of interest.

2、Which of the following statements about statistical concepts is least accurate?

A) A frequency distribution is a tabular display of data summarized into a relatively small number of intervals.

B) An interval is a set of return values within which an observation falls.

C) A sample contains all members of a specified group, but a population contains only a subset.

D) A parameter is any descriptive measure of a population characteristic.

The correct answer is C

A population is defined as all members of a specified group, but a sample is a subset of a population.

AIM 3: Define and distinguish between point estimate, estimation interval.

1、Which of the following statements about sampling and estimation is most accurate?

A) The standard deviation of the distribution of the sample means is the standard error of the residual.

B) The standard error of the sample means when the standard deviation of the population is unknown equals s / √n, where s = sample standard deviation.

C) The standard error of the sample means when the standard deviation of the population is known equals σ / √n, where σ = sample standard deviation adjusted by n ? 1.

D) The probability that a parameter lies within a range of estimated values is given by α.

The correct answer is B

The probability that a parameter lies within a range of estimated values is given by 1 ? σ. The standard deviation of the distribution of the sample means is the standard error of the sample mean. The term residual is used during the discussion of regression that occurs later in this study session. The standard error of the sample means when the standard deviation of the population is known equals σ / √n, where σ = population standard deviation.

2、A range of estimated values within which the actual value of a population parameter will lie with a given probability of 1 ? α is a(n):

A) α percent point estimate.

B) (1 ? α) percent confidence interval.

C) α percent confidence interval.

D) (1 ? α) percent cross-sectional point estimate.

The correct answer is B

A 95% confidence interval for the population mean (α = 5% is the p-value), for example, is a range of estimates within which the actual value of the population mean will lie with a probability of 95%. Point estimates, on the other hand, are single (sample) values used to estimate population parameters. There is no such thing as a α% point estimate or a (1 ? α)% cross-sectional point estimate.

3、Which of the following statements about sampling and estimation is most accurate?

A) A confidence interval estimate consists of a range of values that bracket the parameter with a specified level of probability, 1 ? β.

B) Time-series data are observations over individual units at a point in time.

C) Cross-sectional data are a set of values of a particular variable in sequential time periods.

D) A point estimate is a single estimate of an unknown population parameter calculated as a sample mean.

The correct answer is Ｄ　

Time-series data are observations taken at specific and equally-spaced points.

Cross-sectional data are a sample of observations taken at a single point in time.

A confidence interval estimate consists of a range of values that bracket the parameter with a specified level of probability, 1 ? α.

４、Which of the following would result in a wider confidence interval? A:

A) higher degree of confidence. 

B) higher alpha level. 

C) higher point estimate. 

D) greater level of significance. 

The correct answer is A

A higher degree of confidence (e.g. 99% instead of 95%) would require a higher reliability factor (2.575 instead of 1.96 assuming a normal distribution). A wider confidence interval corresponds to a lower alpha significance level and the point estimate does not affect the width of the confidence interval.

5、Which of the following statements regarding confidence intervals is most accurate?

A) The higher the alpha level, the wider the confidence interval.

B) The lower the alpha level, the wider the confidence interval. 

C) The relationship between the alpha level and the confidence interval cannot be ascertained. 

D) The lower the degree of confidence, the wider the confidence interval.

The correct answer is B

A higher degree of confidence requires a wider confidence interval. The degree of confidence is equal to one minus the alpha level, and so the wider the confidence interval, the higher the degree of confidence and the lower the alpha level. Note that the lower alpha level requires a higher reliability factor which results in the wider confidence interval.

AIM 7: Define and list the properties of point estimators and distinguish between unbiased and biased estimators.

1、The sample mean is an unbiased estimator of the population mean because the:

A) sampling distribution of the sample mean has the smallest variance of any other unbiased estimators of the population mean.

B) expected value of the sample mean is equal to the population mean.

C) sample mean provides a more accurate estimate of the population mean as the sample size increases.

D) sampling distribution of the sample mean is normal.

The correct answer is B

An unbiased estimator is one for which the expected value of the estimator is equal to the parameter you are trying to estimate.

AIM 8: Define an efficient estimator and consistent estimator.

1、The sample mean is a consistent estimator of the population mean because the:

A) expected value of the sample mean is equal to the population mean.

B) sampling distribution of the sample mean has the smallest variance of any other unbiased estimators of the population mean.

C) sample mean provides a more accurate estimate of the population mean as the sample size increases.

D) sampling distribution of the sample mean is normal.

The correct answer is C

A consistent estimator provides a more accurate estimate of the parameter as the sample size increases.

2、If the variance of the sampling distribution of an estimator is smaller than all other unbiased estimators of the parameter of interest, the estimator is:

A) efficient.

B) reliable.

C) unbiased.

D) consistent.

The correct answer is A

By definition.

3、If Estimator A is a more efficient estimator than Estimator B, it will have:

A) a smaller mean and the same variance. 

B) the same mean and a smaller variance. 

C) a smaller mean and a larger variance. 

D) the same mean and a larger variance.

The correct answer is B

The more efficient estimator is the one that has the smaller variance, given that they both have the same mean.

AIM 9: Define Best Linear Unbiased Estimator.

1、Shawn Choate is thinking about his graduate thesis. Still in the preliminary stage, he wants to choose a variable of study that has the most desirable statistical properties. The statistic he is presently considering has the following characteristics:

?            The expected value of the sample mean is equal to the population mean.

?            The variance of the sampling distribution is smaller than that for other estimators of the parameter.

?            As the sample size increases, the standard error of the sample mean rises and the sampling distribution is centered more closely on the mean.

?            Select the best choice. Choate’s estimator is:

A) unbiased, efficient, and consistent.

B) efficient and consistent.

C) unbiased and consistent.

D) unbiased and efficient.

The correct answer is D

The estimator is unbiased because the expected value of the sample mean is equal to the population mean. The estimator is efficient because the variance of the sampling distribution is smaller than that for other estimators of the parameter.

The estimator is not consistent. To be consistent, as the sample size increases, the standard error of the sample mean should fall and the sampling distribution will be centered more closely on the mean. A consistent estimator provides a more accurate estimate of the parameter as the sample size increases.

AIM 5: Define, calculate and interpret confidence interval, confidence coefficient, upper limit, lower limit, random interval.

1、The average U.S. dollar/Euro exchange rate from a sample of 36 monthly observations is $1.00/Euro. The population variance is 0.49. What is the 95% confidence interval for the mean U.S. dollar/Euro exchange rate?

A) $0.7713 to $1.2287.

B) $0.5100 to $1.4900.

C) $0.8075 to $1.1925.

D) $0.8657 to $1.1343.

The correct answer is A

The population standard deviation is the square root of the variance (√0.49 = 0.7). Because we know the population standard deviation, we use the z-statistic. The z-statistic reliability factor for a 95% confidence interval is 1.960. The confidence interval is $1.00 ± 1.960($0.7 / √36) or $1.00 ± $0.2287.

2、A sample of size 25 is selected from a normal population. This sample has a mean of 15 and the population variance is 4.

Using this information, construct a 95% confidence interval for the population mean, m.

A) 15 ± 1.96(0.4).

B) 15 ± 1.96(2).

C) 15 ± 1.96(0.8).

D) 15 ± 1.96(4).

The correct answer is A

Because we can compute the population standard deviation, we use the z-statistic.  A 95% confidence level is constructed by taking the population mean and adding and subtracting the product of the z-statistic reliability (zα/2) factor times the known standard deviation of the population divided by the square root of the sample size (note that the population variance is given and its positive square root is the standard deviation of the population): x ± zα/2 × ( σ / n1/2) = 15 ± 1.96 × (41/2 / 251/2) = 15 ± 1.96 × (0.4).

3、The approximate 99% confidence interval for the population mean based on a sample of 60 returns with a mean of 7% and a sample standard deviation of 25% is closest to:

A) 1.584% to 14.584%.

B) -1.584% to 15.584%.

C) 0.546% to 13.454%.

D) 1.546% to 13.454%.

The correct answer is B

The standard error for the mean = s / (n)0.5 = 25% / (60)0.5 = 3.227%. The critical value from the t-table should be based on 60 ? 1 = 59 df. Since the standard tables do not provide the critical value for 59 df the closest available value is for 60 df. This leaves us with an approximate confidence interval. Based on 99% confidence and df = 60, the critical t-value is 2.660. Therefore the 99% confidence interval is approximately: 7% ± 2.660(3.227) or 7% ± 8.584% or -1.584% to 15.584%.

If you use a z-statistic, the confidence interval is 7% ± 2.58(3.227) = -1.326% to 15.326%, which is closest to the correct choice.

4、A nursery sells trees of different types and heights. Suppose that 75 pine trees are sold for planting at City Hall. These 75 trees average 60 inches in height with a standard deviation of 16 inches.

Using this information, construct a 95% confidence interval for the mean height of all trees in the nursery.

A) 60 + 1.96(1.85).

B) 60 + 1.96(16).

C) 0.8 + 1.96(16).

D) 0.8 + 1.96(1.85).

The correct answer is A

Because we know the population standard deviation, we use the z-statistic. A 95% confidence level is constructed by taking the population mean and adding and subtracting the product of the z-statistic reliability (zα/2) factor times the known standard deviation of the population divided by the square root of the sample size: x ± zα/2 × ( σ / n1/2) = 60 ± (1.96) × (16 / 751/2) = 60 ± (1.96) × (16 / 8.6603) = 60 ± (1.96) × (1.85).

5、What is the appropriate test statistic for constructing confidence intervals for the population mean of a normal distribution when the population variance is unknown?

A) The t-statistic at α/2 with n degrees of freedom.

B) The z-statistic with n – 1 degrees of freedom.

C) The z-statistic at α with n degrees of freedom.

The correct answer is D

Use the t-statistic at α/2 and n – 1 degrees of freedom when the population variance is unknown, regardless of sample size.

6、What is the appropriate test statistic for constructing confidence intervals for the population mean of a nonnormal distribution when the population variance is unknown and the sample size is large (n ≥ 30)?

A) The z-statistic at α with n degrees of freedom.

B) The t-statistic at α with 29 degrees of freedom.

C) The z-statistic or the t-statistic.

D) The t-statistic at α/2 with n degrees of freedom.

The correct answer is C

When the sample size is large, and the central limit theorem can be relied upon to assure a sampling distribution that is normal, either the t-statistic or the z-statistic is acceptable for constructing confidence intervals for the population mean. However, the t-statistic will provide a more conservative range (wider) at a given level of significance.

7、The 95 percent confidence interval of the sample mean of the price earnings ratio for all traded stocks is 19 to 44. There are over 5,000 traded stocks and the sample size of this test is 100. Given that the expected value of the price earnings ratio is 31.5, the standard error of the ratio is closest to:

A) 1.96.

B) 2.58.

C) 12.50.

D) 6.38.

The correct answer is

The confidence interval is 31.5 ± 1.96x, where x is the standard error. If we take the upper bound, we know that 31.5 +/– 1.96x = 44, or 1.96x = 12.5. Hence, x = 6.38.

8、A random sample of 100 technology stocks earned an average of 10%. Assuming the distribution of equity returns is normal and the population standard deviation is 5%, the 95% confidence interval for the population mean is:

A) 5.00% to 15.00%.

B) 9.02% to 10.98%.

C) 9.50% to 10.50%.

D) 9.91% to 10.90%.

The correct answer is B

Zα / 2 = Z0.025 = 1.96. So, 0.1 +/?1.96(0.05 / 10) = 9.02% to 10.98%.

AIM 10: Explain the process of hypothesis testing.

1、Which of the following statements about testing a hypothesis using a Z-test is least accurate?

A) A Type I error is rejecting the null hypothesis when it is actually true.

B) The calculated Z-statistic determines the appropriate significance level to use.

C) If the calculated Z-statistic lies outside the critical Z-statistic range, the null hypothesis can be rejected.

D) The confidence interval for a two-tailed test of a population mean at the 5% level of significance is that the sample mean falls between ±1.96 σ/√n of the null hypothesis value.

The correct answer is B

The significance level is chosen before the test so the calculated Z-statistic can be compared to an appropriate critical value.

2、Which of the following statements about hypothesis testing is most accurate?

A) A hypothesized mean of 3, a sample mean of 6, and a standard error of the sampling means of 2 give a sample Z-statistic of 1.5.

B) A Type I error is rejecting the null hypothesis when it is true, and a Type II error is accepting the alternative hypothesis when it is false.

C) When the critical Z-statistic is greater than the sample Z-statistic in a two-tailed test, reject the null hypothesis and accept the alternative hypothesis.

D) A two-tailed test on a large sample with a significance level of 0.01 has confidence intervals of ±1.96 standard errors.

The correct answer is A

The 0.01 level of significance has confidence intervals of ± 2.58 standard errors. A Type II error is wrongly accepting the null hypothesis. The null hypothesis should be rejected when the sample Z-statistic is greater than the critical Z-statistic.

3、Which of the following statements about hypothesis testing is most accurate?

A) If you can disprove the null hypothesis, then you have proven the alternative hypothesis.

B) To test the claim that X is greater than zero, the null hypothesis would be H0: X > 0.

C) The power of a test is one minus the probability of a Type I error.

D) The probability of a Type I error is equal to the significance level of the test.

The correct answer is D

The probability of getting a test statistic outside the critical value(s) when the null is ture is the level of significance and is the probability of a Type I error. The power of a test is 1 minus the probability of a Type II error. Hypothesis testing does not prove a hypothesis, we either reject the null or fail to reject it. The appropriate null would be "X ≤ 0" with "X > 0" as the alternative hypothesis.

4、Which of the following statements least describes the procedure for testing a hypothesis?

A) Develop a hypothesis, compute the test statistic, and make a decision.

B) Select the level of significance, formulate the decision rule, and make a decision.

C) Select the level of significance, compute the test statistic, and make a decision.

D) Compute the sample value of the test statistic, set up a rejection (critical) region, and make a decision.

The correct answer is D

Depending upon the author there can be as many as seven steps in hypothesis testing which are:

Stating the hypotheses.

Identifying the test statistic and its probability distribution.

Specifying the significance level.

Stating the decision rule.

Collecting the data and performing the calculations.

Making the statistical decision.

Making the economic or investment decision.

5、In the process of hypothesis testing, what is the proper order for these steps?

A) Specify the level of significance. State the hypotheses. Make a decision. Collect the sample and calculate the sample statistics.

B) State the hypotheses. Collect the sample and calculate the sample statistics. Make a decision. Specify the level of significance.

C) State the hypotheses. Specify the level of significance. Collect the sample and calculate the test statistics. Make a decision.

D) Collect the sample and calculate the sample statistics. State the hypotheses. Specify the level of significance. Make a decision.

The correct answer is C

The hypotheses must be established first. Then the test statistic is chosen and the level of significance is determined. Following these steps, the sample is collected, the test statistic is calculated, and the decision is made.

AIM 11: Define and interpret the null hypothesis, the alternative hypothesis.

1、An analyst conducts a two-tailed z-test to determine if small cap returns are significantly different from 10%. The sample size was 200. The computed z-statistic is 2.3. Using a 5% level of significance, which statement is most accurate?

A) You cannot determine what to do with the information given.

B) A sample size of 200 indicates that we should fail to reject the null.

C) Reject the null hypothesis and conclude that small cap returns are significantly different from 10%.

D) Fail to reject the null hypothesis and conclude that small cap returns are close enough to 10% that we cannot say they are significantly different from 10%.

The correct answer is C

At the 5% level of significance the critical z-statistic for a two-tailed test is 1.96 (assuming a large sample size). The null hypothesis is H0: x = 10%. The alternative hypothesis is HA: x ≠ 10%. Because the computed z-statistic is greater than the critical z-statistic (2.33 > 1.96), we reject the null hypothesis and we conclude that small cap returns are significantly different than 10%.

2、An analyst conducts a two-tailed test to determine if mean earnings estimates are significantly different from reported earnings. The sample size is greater than 25 and the computed test statistic is 1.25. Using a 5% significance level, which of the following statements is most accurate?

A) The appropriate test to apply is a two-tailed chi-square test.

B) To test the null hypothesis, the analyst must determine the exact sample size and calculate the degrees of freedom for the test.

C) The analyst should fail to reject the null hypothesis and conclude that the earnings estimates are not significantly different from reported earnings.

D) The analyst should reject the null hypothesis and conclude that the earnings estimates are significantly different from reported earnings.

The correct answer is C

The null hypothesis is that earnings estimates are equal to reported earnings. To reject the null hypothesis, the calculated test statistic must fall outside the two critical values. IF the analyst tests the null hypothesis with a z-statistic, the crtical values at a 5% confidence level are ±1.96. Because the calculated test statistic, 1.25, lies between the two critical values, the analyst should fail to reject the null hypothesis and conclude that earnings estimates are not significantly different from reported earnings. If the analyst uses a t-statistic, the upper critical value will be even greater than 1.96, never less, so even without the exact degrees of freedom the analyst knows any t-test would fail to reject the null.

3、An analyst is testing to see if the mean of a population is less than 133. A random sample of 50 observations had a mean of 130. Assume a standard deviation of 5. The test is to be made at the 1% level of significance.

The null hypothesis is:

A)    μ > 133.

B)    μ ≤ 133.

C)   μ = 133.

D)   μ ≥ 133.

The correct answer is D

The null hypothesis is the hypothesis that the researcher wants to reject. Here the hypothesis that is being looked for is that the mean of a population is less than 133. The null hypothesis is that the mean is greater than or equal to 133. The question is whether the null hypothesis will be rejected in favor of the alternative hypothesis that the mean is less than 133.

The calculated test statistic is:

A) -4.24.

B) +1.33.

C) -1.33.

D) -3.00.

The correct answer is A

A test statistic is calculated by subtracting the hypothesized parameter from the parameter that has been estimated and dividing the difference by the standard error of the sample statistic. Here, the test statistic = (sample mean – hypothesized mean) / ((sample standard deviation / (sample size)1/2)) = (130 – 133) / (5 / 501/2) = (-3) / (5 / 7.0711) = -4.24.

The critical value is:

A) 2.17.

B) -2.38.

C) 2.47.

D) -2.33.

The correct answer is D

This is a one-tailed test with a significance level of 0.01. The critical value for a one-tailed test at a 1% level of significance is -2.33.

You should:

A) accept the null hypothesis.

B) reject the null hypothesis.

C) reject the alternative hypothesis.

D) Cannot be determined with the information given.

The correct answer is B

The calculated test statistic of -4.24 falls to the left of the z-statistic of -2.33, and is in the rejection region. Thus, the null hypothesis is rejected and the conclusion is that the population mean is less than 133.

4、Susan Bellows is comparing the return on equity for two industries. She is convinced that the return on equity for the discount retail industry (DR) is greater than that of the luxury retail (LR) industry. What are the hypotheses for a test of her comparison of return on equity?

A) H0: μDR = μLR versus Ha: μDR ≠ μLR.

B) H0: μDR ≠ μLR versus Ha: μDR = μLR.

C) H0: μDR = μLR versus Ha: μDR < μLR.

D) H0: μDR ≤ μLR versus Ha: μDR > μLR.

The correct answer is D

The alternative hypothesis is determined by the theory or the belief. The researcher specifies the null as the hypothesis that she wishes to reject (in favor of the alternative). Note that this is a one-sided alternative because of the “greater than” belief.

AIM 12: Distinguish between one-sided and two-sided hypotheses.

1、Using the following hypothesis and data:

?            H0: a = b and H1: a ≠ b

?            The critical Z-statistic is 2.58

?            The calculated Z-statistic is 4.1

An analyst should:

A) Reject the null hypothesis and conclude that a = b.

B) Reject the null hypothesis and conclude that a is significantly different than b.

C) Reject the alternative hypothesis and conclude that a = b.

D) Fail to reject the null hypothesis and conclude that we cannot say that a is significantly different than b.

The correct answer is B

When the calculated Z > the critical Z (4.1 > 2.58), the null hypothesis should be rejected and the conclusion is made that a is not equal to b.

2、Which of the following statements is FALSE?

A) For a one-tailed test at the 5% level of significance, the critical z-value is 1.645.

B) For a two-tailed test at the 1% level of significance, the critical z-values are +/?2.33.

C) The standard error of the sample mean may be expressed as s / √n.

D) The calculated z-statistic for a sample mean is (x ? μ) / (σ / √n).

The correct answer is B

For a two-tailed test at a 1% level of significance, the critical values are +/?2.58.

AIM 14: Define, calculate and interpret the test of significance approach to hypothesis testing.

1、In a two-tailed test of a hypothesis concerning whether a population mean is zero, Jack Olson computes a t-statistic of 2.7 based on a sample of 20 observations where the distribution is normal. If a 5% significance level is chosen, Olson should:

A) not make a conclusion pending additional observations.

B) reject the null hypothesis and conclude that the population mean is not significantly different from zero.

C) fail to reject the null hypothesis that the population mean is not significantly different from zero.

D) reject the null hypothesis and conclude that the population mean is significantly different from zero.

The correct answer is D

At a 5% significance level, the critical t-statistic using the Student’s t-distribution table for a two-tailed test and 19 degrees of freedom (sample size of 20 less 1) is ± 2.093 (with a large sample size the critical z-statistic of 1.960 may be used). Because the critical t-statistic of 2.093 is to the left of the calculated t-statistic of 2.7, meaning that the calculated t-statistic is in the rejection range, we reject the null hypothesis and we conclude that the population mean is significantly different from zero.

2、A survey is taken to determine whether the average starting salaries of CFA charterholders is equal to or greater than $59,000 per year. What is the test statistic given a sample of 135 newly acquired CFA charterholders with a mean starting salary of $64,000 and a standard deviation of $5,500?

A) 0.91.

B) -10.56.

C) -0.91.

D) 10.56.

The correct answer is D

With a large sample size (135) the z-statistic is used. The z-statistic is calculated by subtracting the hypothesized parameter from the parameter that has been estimated and dividing the difference by the standard error of the sample statistic. Here, the test statistic = (sample mean – hypothesized mean) / (population standard deviation / (sample size)1/2) = (X ? μ) / (σ / n1/2) = (64,000 – 59,000) / (5,500 / 1351/2) = (5,000) / (5,500 / 11.62) = 10.56.

3、Margo Hinsdale is testing the null hypothesis that the population mean is less than or equal to 45. A random sample of 81 observations selected from this population produced a mean of 46.3. The population has a standard deviation of 4.5.

The value of the appropriate test statistic for the test of the population mean is:

A) z = –2.75.

B) t = 3.84.

C) t = 4.60.

The correct answer is

The population variance is known and the sample size is large. The test statistic is:

4、At a 1 percent level of significance, the correct decision is to:

A) accept the null hypothesis.

B) fail to reject the null hypothesis.

C) neither reject nor fail to reject the null hypothesis.

D) reject the null hypothesis.

The correct answer is D

Decision rule: reject H0 if zcomputed > zcritical. Therefore, reject the null hypothesis because the computed test statistic of 2.60 (see the answer to Part 1) exceeds the critical z-value of 2.33.

5、If the sample size is greater than 30 and population variance is unknown, the appropriate test for the sample mean is the:

A) t-test.

B) z-test.

C) t-test or z-test.

D) p-test or F-test.

The correct answer is C

The central limit theorem makes it appropriate to use the z-test with an unknown variance if the sample size is large enough (n ≥ 30), regardless of the distribution of the population. Since the t- and the z-distributions converge as sample size increases, either test is appropriate, although the t-test is a more conservative estimate.

6、A return series with 250 observations has a sample mean of 10 percent and a standard deviation of 15 percent. The standard error of the sample mean is closest to:

A) 0.06.

B) 0.95.

C) 15.80.

D) 3.87.

The correct answer is B

The standard error of the sample mean is the standard deviation of the sample divided by the square root of the number of observations in the sample. In this case, (15 / √250) = 0.95.

7、The mean daily return for an equity portfolio over 60 months is 1.5 percent. The standard deviation is 3.0 percent. The value of the test statistic to test the hypothesis that mean monthly return is equal to zero is closest to:

A) 0.50.

B) 30.00.

C) 3.87.

D) 2.19.

The correct answer is C

z = (1.5% - 0.0%) / [(3.0% / √60)] = 3.87

8、The mean equity risk premium over a 40-year period is equal to 8.0 percent. The standard deviation of the sample is 12 percent. The standard error of the sample mean is closest to:

A) 0.30%.

B) 1.90%.

C) 1.26%.

D) 8.00%.

The correct answer is B

Note the size of the sample here is the number of years.

σX = 12 / √40 = 1.90%

9、Maria Huffman is the Vice President of Human Resources for a large regional car rental company. Last year, she hired Graham Brickley as Manager of Employee Retention. Part of the compensation package was the chance to earn one of the following two bonuses: if Brickley can reduce turnover to less than 30%, he will receive a 25% bonus. If he can reduce turnover to less than 25%, he will receive a 50% bonus (using a significance level of 10%). The population of turnover rates is normally distributed. The population standard deviation of turnover rates is 1.5%. A recent sample of 100 branch offices resulted in an average turnover rate of 24.2%. Which of the following statements is most accurate?

A) Brickley should not receive either bonus.

B) For the 25% bonus level, the test statistic is -10.66.

C) For the 50% bonus level, the critical value is -1.65 and Huffman should give Brickley a 50% bonus.

D) For the 50% bonus level, the test statistic is -5.33 and Huffman should give Brickley a 50% bonus.

The correct answer is D

Using the process of Hypothesis testing:

Step 1: State the Hypothesis. For 25% bonus level - Ho: m ≥ 30% Ha: m < 30%; For 50% bonus level - Ho: m ≥ 25% Ha: m < 25%.

Step 2: Select Appropriate Test Statistic. Here, we have a normally distributed population with a known variance (standard deviation is the square root of the variance) and a large sample size (greater than 30.) Thus, we will use the z-statistic.

Step 3: Specify the Level of Significance. α = 0.10.

Step 4: State the Decision Rule. This is a one-tailed test. The critical value for this question will be the z-statistic that corresponds to an α of 0.10, or an area to the left of the mean of 40% (with 50% to the right of the mean). Using the z-table (normal table), we determine that the appropriate critical value = -1.28 (Remember that we highly recommend that you have the “common” z-statistics memorized!) Thus, we will reject the null hypothesis if the calculated test statistic is less than -1.28.

Step 5: Calculate sample (test) statistics. Z (for 50% bonus) = (24.2 – 25) / (1.5 / √ 100) = ?5.333. Z (for 25% bonus) = (24.2 – 30) / (1.5 / √ 100) = ?38.67.

Step 6: Make a decision. Reject the null hypothesis for both the 25% and 50% bonus level because the test statistic is less than the critical value. Thus, Huffman should give Soberg a 50% bonus.

The other statements are false. The critical value of –1.28 is based on the significance level, and is thus the same for both the 50% and 25% bonus levels.

10、A bottler of iced tea wishes to ensure that an average of 16 ounces of tea is in each bottle. In order to analyze the accuracy of the bottling process, a random sample of 150 bottles is taken.  Using a t-distributed test statistic of -1.09 and a 5% level of significance, the bottler should:

A) not reject the null hypothesis and conclude that bottles contain an average 16 ounces of tea.

B) reject the null hypothesis and conclude that bottles contain an average 16 ounces of tea.

C) reject the null hypothesis and conclude that bottles do not contain an average of 16 ounces of tea.

D) not reject the null hypothesis and conclude that bottles do not contain an average of 16 ounces of tea.

The correct answer is A

Ho: μ = 16; Ha: μ ≠ 16. Do not reject the null since |t| = 1.09 < 1.96 (critical value).

11、Brian Ci believes that the average return on equity in the airline industry, μ, is less than 5%. What are the appropriate null (H0) and alternative (Ha) hypotheses to test this belief?

A) H0: μ < 0.05 versus Ha: μ > 0.05.

B) H0: μ > 0.05 versus Ha: μ < 0.05.

C) H0: μ ≥ 0.05 versus Ha: μ < 0.05.

D) H0: μ < 0.05 versus Ha: μ ≥ 0.05.

The correct answer is C

The alternative hypothesis is determined by the theory or the belief. The researcher specifies the null as the hypothesis that he wishes to reject (in favor of the alternative). Note that this is a one-sided alternative because of the "less than" belief.

12、Robert Patterson, an options trader, believes that the return on options trading is higher on Mondays than on other days. In order to test his theory, he formulates a null hypothesis. Which of the following would be an appropriate null hypothesis? Returns on Mondays are:

A) greater than returns on other days.

B) less than returns on other days.

C) not greater than returns on other days.

D) not less than returns on other days.

The correct answer is C

An appropriate null hypothesis is one that the researcher wants to reject. If Patterson believes that the returns on Mondays are greater than on other days, he would like to reject the hypothesis that the opposite is true–that returns on Mondays are not greater than returns on other days.

13、Given the following hypothesis:

?            The null hypothesis is H0 : μ = 5

?            The alternative is H1 : μ ≠ 5

?            The mean of a sample of 17 is 7

?            The population standard deviation is 2.0

What is the calculated z-statistic?

A) 4.00.

B) 8.00.

C) 8.25.

D) 4.12.

The correct answer is D

The z-statistic is calculated by subtracting the hypothesized parameter from the parameter that has been estimated and dividing the difference by the standard error of the sample statistic. Here, the test statistic = (sample mean ? hypothesized mean) / (population standard deviation / (sample size)1/2 = (X ? μ) / (σ / n1/2) = (7 ? 5) / (2 / 171/2) = (2) / (2 / 4.1231) = 4.12.

14、The mean monthly return for an equity portfolio over 60 months is 1.5%. The standard deviation is 3.0%. The value of the test statistic to test the hypothesis that mean monthly return is equal to zero is closest to:

A) 30.00

B) 3.87.

C) 0.50.

D) 2.19.

The correct answer is B

AIM 6: Define, calculate and interpret type I and type II errors.

1、Which of the following is the correct sequence of events for testing a hypothesis?

A) State the hypothesis, formulate the decision rule, select the level of significance, compute the test statistic, and make a decision.

B) State the hypothesis, select the level of significance, compute the test statistic, formulate the decision rule, and make a decision.

C) State the hypothesis, select the level of significance, formulate the decision rule, compute the test statistic, and make a decision.

D) State the hypothesis, formulate the decision rule, compute the test statistic, select the level of significance, and make a decision.

The correct answer is C

Depending upon the author there can be as many as seven steps in hypothesis testing which are:

Stating the hypotheses.

Identifying the test statistic and its probability distribution.

Specifying the significance level.

Stating the decision rule.

Collecting the data and performing the calculations.

Making the statistical decision.