leiyou

 

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.

leiyou

 

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.

leiyou

 

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%.

leiyou

 

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%.

leiyou

 

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.

leiyou

 

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.

leiyou

 

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.

z	0.00	0.01	0.02	0.03	0.04	0.05	0.06
0.0	0.0000	0.0040	0.0080	0.0120	0.0160	0.0199	0.0239
0.1	0.0398	0.0438	0.0478	0.0517	0.0557	0.0596	0.0636
0.2	0.0793	0.0832	0.0871	0.0910	0.0948	0.0987	0.1026
0.3	0.1179	0.1217	0.1255	0.1293	0.1331	0.1368	0.1406
|	|	|	|	|	|	|	|
1.7	0.4554	0.4564	0.4573	0.4582	0.4591	0.4599	0.4608
1.8	0.4641	0.4649	0.4656	0.4664	0.4671	0.4678	0.4686
1.9	0.4713	0.4719	0.4726	0.4732	0.4738	0.4744	0.4750
2.0	0.4772	0.4778	0.4783	0.4788	0.4793	0.4798	0.4803
2.1	0.4821	0.4826	0.4830	0.4834	0.4838	0.4842	0.4846
2.2	0.4861	0.4864	0.4868	0.4871	0.4875	0.4878	0.4881
2.3	0.4893	0.4896	0.4898	0.4901	0.4904	0.4906	0.4909
2.4	0.4918	0.4920	0.4922	0.4925	0.4927	0.4929	0.4931

The null hypothesis is:

A)    μ > 133.

B)    μ ≤ 133.

C)   μ = 133.

D)   μ ≥ 133.

leiyou

 

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.

leiyou

 

The calculated test statistic is:

A) -4.24.

B) +1.33.

C) -1.33.

D) -3.00.

leiyou

 

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.