Q1. A researcher is testing whether the average age of employees in a large firm is statistically different from 35 years (either above or below). A sample is drawn of 250 employees and the researcher determines that the appropriate critical value for the test statistic is 1.96. The value of the computed test statistic is 4.35. Given this information, which of the following statements is least accurate? The test:

A)   indicates that the researcher will reject the null hypothesis.

B)   has a significance level of 95%.

C)   indicates that the researcher is 95% confident that the average employee age is different than 35 years.

Q2. A pitching machine is calibrated to deliver a fastball at a speed of 98 miles per hour. Every day, a technician samples the speed of twenty-five fastballs in order to determine if the machine needs adjustment. Today, the sample showed a mean speed of 99 miles per hour with a standard deviation of 1.75 miles per hour. At a 95% confidence level, what is the z-value in relation to the critical value?

A)   The z-value exceeds the critical value by 0.9 standard deviations.

B)   The critical value exceeds the z-value by 1.3 standard deviations.

C)   The z-value exceeds the critical value by 1.5 standard deviations.

Q3. For a two-tailed test of hypothesis involving a z-distributed test statistic and a 5% level of significance, a calculated z-statistic of 1.5 indicates that:

A)   the null hypothesis is rejected.

B)   the null hypothesis cannot be rejected.

C)   the test is inconclusive.

答案和详解如下：

Q1. A researcher is testing whether the average age of employees in a large firm is statistically different from 35 years (either above or below). A sample is drawn of 250 employees and the researcher determines that the appropriate critical value for the test statistic is 1.96. The value of the computed test statistic is 4.35. Given this information, which of the following statements is least accurate? The test:

A)   indicates that the researcher will reject the null hypothesis.

B)   has a significance level of 95%.

C)   indicates that the researcher is 95% confident that the average employee age is different than 35 years.

Correct answer is B)

This test has a significance level of 5%. The relationship between confidence and significance is: significance level = 1 − confidence level. We know that the significance level is 5% because the sample size is large and the critical value of the test statistic is 1.96 (2.5% of probability is in both the upper and lower tails).

Q2. A pitching machine is calibrated to deliver a fastball at a speed of 98 miles per hour. Every day, a technician samples the speed of twenty-five fastballs in order to determine if the machine needs adjustment. Today, the sample showed a mean speed of 99 miles per hour with a standard deviation of 1.75 miles per hour. At a 95% confidence level, what is the z-value in relation to the critical value?

A)   The z-value exceeds the critical value by 0.9 standard deviations.

B)   The critical value exceeds the z-value by 1.3 standard deviations.

C)   The z-value exceeds the critical value by 1.5 standard deviations.

Correct answer is A)

z = (99 – 98) / (1.75 / √25) = 2.86. The critical value for a two-tailed test at the 95% confidence level is ± 1.96 standard deviations. Therefore, the z-value exceeds the critical value by 0.9 standard deviations.

Q3. For a two-tailed test of hypothesis involving a z-distributed test statistic and a 5% level of significance, a calculated z-statistic of 1.5 indicates that:

A)   the null hypothesis is rejected.

B)   the null hypothesis cannot be rejected.

C)   the test is inconclusive.

Correct answer is B)

For a two-tailed test at a 5% level of significance the calculated z-statistic would have to be greater than the critical z value of 1.96 for the null hypothesis to be rejected.

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