leiyou

 

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.

leiyou

 

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.

leiyou

 

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.

leiyou

 

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.

leiyou

 

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.

D) z = 2.60.

leiyou

 

The correct answer is

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

[attach]13860[/attach]

leiyou

 

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.

leiyou

 

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.

leiyou

 

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.

leiyou

 

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.