Question 6 [10 points]
A sample of 53 observations has a mean of 95 and a population standard deviation of 7. A second sample of 37 has a mean of 98 and a population standard deviation of 6. Conduct a
z-test about a difference in sample means using a 0.04 significance level and the following hypotheses:
H0: μ1 - μ2 ≥ 0 H1: μ1 - μ2 < 0
| a) | What is the correct decision rule? | Reject H0 in favour of H1 if the computed value of the statistic is greater than 2.05. | | Reject H0 in favour of H1 if the computed value of the statistic is less than -2.05 or greater than 2.05. | | Reject H0 in favour of H1 if the computed value of the statistic is between -2.05 and 2.05. | | Reject H0 in favour of H1 if the computed value of the statistic is less than -1.75. | | Reject H0 in favour of H1 if the computed value of the statistic is between -1.75 and 1.75. | | Reject H0 in favour of H1 if the computed value of the statistic is less than -1.75 or greater than 1.75. | | None of the above. |
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b) Compute the value of the test statistic.
For full marks your answer should be accurate to at least two decimal places.
Test statistic: 0
| c) | What is your decision regarding H0? | There is sufficient evidence, at the given significance level, to reject H0, and accept H1 or at least there is not enough evidence to reject H1. | | There is insufficient evidence, at the given significance level, to reject H0. | | There is insufficient evidence to reject or not reject the null hypothesis. |
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d) Calculate the
p-value.
For full marks your answer should be accurate to at least four decimal places.
P-value: 0
Question 7 [10 points]
A sample of 37 observations has a mean of 102 and a population standard deviation of 5. A second sample of 57 has a mean of 99 and a population standard deviation of 6. Conduct a
z-test about a difference in sample means using a 0.03 significance level and the following hypotheses:
H0: μ1 - μ2 ≤ 0 H1: μ1 - μ2 > 0
| a) | What is the correct decision rule? | Reject H0 in favour of H1 if the computed value of the statistic is between -1.88 and 1.88. | | Reject H0 in favour of H1 if the computed value of the statistic is less than 1.88. | | Reject H0 in favour of H1 if the computed value of the statistic is less than -1.88 or greater than 1.88. | | Reject H0 in favour of H1 if the computed value of the statistic is less than -2.17 or greater than 2.17. | | Reject H0 in favour of H1 if the computed value of the statistic is between -2.17 and 2.17. | | Reject H0 in favour of H1 if the computed value of the statistic is greater than 1.88. | | None of the above. |
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b) Compute the value of the test statistic.
For full marks your answer should be accurate to at least two decimal places.
Test statistic: 0
| c) | What is your decision regarding H0? | There is sufficient evidence, at the given significance level, to reject H0, and accept H1 or at least there is not enough evidence to reject H1. | | There is insufficient evidence, at the given significance level, to reject H0. | | There is insufficient evidence to reject or not reject the null hypothesis. |
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d) Calculate the
p-value.
For full marks your answer should be accurate to at least four decimal places.
P-value: