Reading 11: Hypothesis Testing - LOS e, (Part 1) ～ Q1-5

答案和详解如下：

1.In order to test if the mean IQ of employees in an organization is greater than 100, a sample of 30 employees is taken. The sample value of the computed z-statistic = 3.4. The appropriate decision at a 5% significance level is to:

A)   reject the null hypotheses and conclude that the population mean is greater than 100.

B)   reject the null hypothesis and conclude that the population mean is equal to 100.

C)   accept the null hypothesis and conclude that the population mean is equal to 100.

D)   reject the null hypothesis and conclude that the population mean is not equal to 100.

The correct answer was A)

H_o:µ ≤ 100; H_a: µ > 100. Reject the null since z = 3.4 > 1.65 (critical value).

2.In a two-tailed hypothesis test, Jack Olson observes a t-statistic of -1.38 based on a sample of 20 observations where the population mean is zero. If you choose a 5 percent significance level, you should:

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

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

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

D)   not make a conclusion.

The correct answer was B)

At a 5 percent 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 -1.38, meaning that the calculated t-statistic is not in the rejection range, we fail to reject the null hypothesis that the population mean is not significantly different from 100.

3.In order to test whether the mean IQ of employees in an organization is greater than 100, a sample of 30 employees is taken and the sample value of the computed test statistic, t_n-1 = 3.4. If you choose a 5 percent significance level you should:

A)   fail to reject the null hypothesis and conclude that the population mean is greater than 100.

B)   reject the null hypothesis and conclude that the population mean is equal to 100.

C)   fail to reject the null hypothesis and conclude that the population mean is less than or equal to 100.

D)   reject the null hypothesis and conclude that the population mean is greater that 100.

The correct answer was D)

At a 5 percent significance level, the critical t-statistic using the Student’s t distribution table for a one-tailed test and 29 degrees of freedom (sample size of 30 less 1) is 1.699 (with a large sample size the critical Z-statistic of 1.645 may be used). Because the calculated t-statistic of 3.4 is greater than the critical t-statistic of 1.699, meaning that the calculated t-statistic is in the rejection range, we reject the null hypothesis and we conclude that the population mean is greater than 100.

4.In a test of the mean of a population, if the population variance is:

A)   known, a z-distributed test statistic is appropriate.

B)   known, a t-distributed test statistic is appropriate.

C)   unknown, a z-distributed test statistic is appropriate.

D)   unknown, a test cannot be performed.

The correct answer was A)

If the population sampled has a known variance, the z-test is the correct test to use. In general, a t-test is used to test the mean of a population when the population variance is unknown. Note that in special cases when the sample is extremely large, the z-test may be used in place of the t-test, but the t-test is considered to be the test of choice when the population variance is unknown.

5.Which of the following statements about test statistics is FALSE? In:

A)   a test of the population mean, if the population variance is unknown and the sample is small, we should use a z-distributed test statistic.

B)   a test of the population mean, if the population variance is unknown, we should use a t-distributed test statistic.

C)   the case of a test of the difference in means of two independent samples, we use a t-distributed test statistic.

D)   the test comparing variances of two normally distributed populations, we use an F-distributed test statistic.

The correct answer was A)

If the population sampled has a known variance, the z-test is the correct test to use. In general, a t-test is used to test the mean of a population when the population is unknown. Note that in special cases when the sample is extremely large, the z-test may be used in place of the t-test, but the t-test is considered to be the test of choice when the population variance is unknown. A t-test is also used to test the difference between two population means while an F-test is used to compare differences between the variances of two populations.