91Ó°ÊÓ

Find the rejection region (for the standardized test statistic) for each hypothesis test. a. \(\quad H 0: \mu=27\) VS. \(H a ; \mu<27\) \(@ \alpha=0.05\). b. \(\quad H 0: \mu=52\) vs. \(H a: \mu \neq 52\) \(@ \alpha=0.05 .\) c. \(\quad H 0: \mu=-105\) VS. Ha: \(\mu>-105\) \(@ \alpha=0.10\). d. \(\quad H 0: \mu=78.8\) VS. Ha: \(\mu \neq 78.8 @ \alpha=0.10\).

State the null and alternative hypotheses for each of the following situations. (That is, identify the correct number \(\mu_{0}\) and write \(H_{0} \cdot \mu=\mu_{0}\) and the appropriate analogous expression for \(H_{a}\).) a. The average July temperature in a region historically has been \(74.5^{\circ} \mathrm{F}\). Perhaps it is higher now. b. The average weight of a female airline passenger with luggage was 145 pounds ten years ago. The FAA believes it to be higher now. c. The average stipend for doctoral students in a particular discipline at a state university is \(\$ 14,756\). The department chairman believes that the national average is higher. d. The average room rate in hotels in a certain region is \(\$ 82.53 .\) A travel agent believes that the average in a particular resort area is different. e. The average farm size in a predominately rural state was 69.4 acres. The secretary of agriculture of that state asserts that it is less today.

Find the rejection region (for the standardized test statistic) for each hypothesis test. Identify the test as left-tailed, right-tailed, or two- tailed. a. \(\quad H 0: \mu=141\) VS. \(H a: \mu<141\) \(@ \alpha=0.20 .\) b. \(\quad H 0: \mu=-54\) VS. \(H a: \mu<-54\) @ \(\alpha=0.05 .\) C. \(\quad H 0: \mu=98.6\) VS. \(H a: \mu \neq 98.6\) \(@ \alpha=0.05 .\) d. \(\quad H 0: \mu=3.8\) VS. \(H a: \mu>3.8\) @ \(\alpha=0.001\)

State the null and alternative hypotheses for each of the following situations. (That is, identify the correct number \(\mu_{0}\) and write \(H_{0} \mu=\mu_{0}\) and the appropriate analogous expression for \(H_{a}\).) a. The average time workers spent commuting to work in Verona five years ago was 38.2 minutes. The Verona Chamber of Commerce asserts that the average is less now. b. The mean salary for all men in a certain profession is \(\$ 58,291\). A special interest group thinks that the mean salary for women in the same profession is different. c. The accepted figure for the caffeine content of an 8 -ounce cup of coffee is \(133 \mathrm{mg}\). A dietitian believes that the average for coffee served in a local restaurants is higher. d. The average yield per acre for all types of corn in a recent year was 161.9 bushels. An economist believes that the average yield per acre is different this year. e. An industry association asserts that the average age of all self-described fly fishermen is 42.8 years. A sociologist suspects that it is higher.

Find the rejection region (for the standardized test statistic) for each hypothesis test. Identify the test as left-tailed, right-tailed, or two- tailed. a. \(\quad H 0: \mu=141\) VS. Ha: \(\mu<141\) \(@ \alpha=0.20\). b. \(\quad H 0: \mu=-54\) vs. Ha: \(\mu<-54 @ \alpha=0.05\). C. \(\quad H 0: \mu=98.6\) VS. \(H a: \mu \neq 98.6 @ \alpha=0.05 .\) d. \(\quad H 0: \mu=3.8\) VS. Ha: \(\mu>3.8 @ \alpha=0.001\).

The mean yield for hard red winter wheat in a certain state is 44.8 bu/acre. In a pilot program a modified growing scheme was introduced on 35 independent plots. The result was a sample mean yield of 45.4 bu/acre with sample standard deviation 1.6 bu/acre, an apparent increase in yield. a. Test at the \(5 \%\) level of significance whether the mean yield under the new scheme is greater than 44.8 bu/acre, using the critical value approach. b. Compute the observed significance of the test. c. Perform the test at the \(5 \%\) level of significance using the \(p\) -value approach. You need not repeat the first three steps, already done in part (a).