Independent random samples of 80 measurements were drawn from two quantitative populations, 1 and 2. Here is a summary of the sample data: Sample 1 Sample 2 Sample Size Sample Mean 80 80 11.6 9.7 Sample variance 27.9 38.4 a. If your research objective is to show that Hi is larger than 42, state the alternative and the null hypotheses that you would choose for a statistical test. b. Calculate the test statistic that you would use for the test in part a. Based on your knowledge of the standard normal distribution, is this a likely or unlikely observation, assuming that Hois true and the two population means are the same? c. p-value approach: Find the p-value for the test. Test for a significant difference in the population means at the 1% significance level.

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1. Independent random samples of 80 measurements were drawn from two quantitative populations,
1 and 2. Here is a summary of the sample data:
Sample 1 Sample 2
Sample Size
80
80
Sample Mean
11.6
9.7
| Sample variance
27.9
38.4
a. If your research objective is to show that Hi is larger than 42, state the alternative and the null hypotheses
that you would choose for a statistical test.
b. Calculate the test statistic that you would use for the test in part a. Based on your knowledge of the standard
normal distribution, is this a likely or unlikely observation, assuming that Ho is true and the two
population means are the same?
c. p-value approach: Find the p-value for the test. Test for a significant difference in the population
means at the 1% significance level.
d. Critical value approach: Find the rejection region when a =0.01. Do the data provide sufficient evidence to
indicate a difference in the population means?
Transcribed Image Text:1. Independent random samples of 80 measurements were drawn from two quantitative populations, 1 and 2. Here is a summary of the sample data: Sample 1 Sample 2 Sample Size 80 80 Sample Mean 11.6 9.7 | Sample variance 27.9 38.4 a. If your research objective is to show that Hi is larger than 42, state the alternative and the null hypotheses that you would choose for a statistical test. b. Calculate the test statistic that you would use for the test in part a. Based on your knowledge of the standard normal distribution, is this a likely or unlikely observation, assuming that Ho is true and the two population means are the same? c. p-value approach: Find the p-value for the test. Test for a significant difference in the population means at the 1% significance level. d. Critical value approach: Find the rejection region when a =0.01. Do the data provide sufficient evidence to indicate a difference in the population means?
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