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SAMPLE PROBLEM A gasoline manufacturer believes a ne w additive will result in more miles per gallon. A la rge number of mileage measurements on the gasoline without the additive have been made by the company under rigorously controlled conditions. The results show a mean of 24.7 miles per gallon and a standard deviation of 4.8. Tests are conducted on a sample of 75 cars using the gasoline plus the additive. The sample mean equals 26.5 miles per gallon. a. Let's assume there is a dequate basis for a one -tailed test. What is the direc- tional alternative hypothesis? b. What is the null hypothesis? c. What is the conclusion? Use or = 0.05, bail- 1. State the hypotheses and select an alpha level Null Hypothesis - Ho: / = population mean Alternative Hypothesis - Hj: / * population mean 2. Draw the normal curve: label the critical value and critical region; determine the critical value refer to the z-table for the critical value 3. Calculate the test statistic US - VN 4. Make a decision regarding Ho assess whether Zot falls within the critical region If kotel 2 kaid. reject the null hypothesis. If not, retain the null hypothesis. ANSWER . State the hypothesis Null hypothesis: The new additive does not increase the number of miles per gallon. The sample with the mean 26.5 is a random sample from a population with population mean less than or equal to 24.7 H: US 24.7 Alternative hypothesis: The new additive increases the number of miles per gallon. Therefore, the sample with the mean 26.5 is a random sample from a population with a population mean that is greater than 24.7 H,: L > 24.7 2. Draw the normal curve, label the critical value and region a = .05qtail Zcrit = 1.645 1.645 (a) One-tailed test3. Calculate the test statistic Given: E = 25.5 a = 4.3 9'1 = 24.? N = T5 XE tll 20m all N ass-24.? 2\"\" = 4.531% Int\": $5343 2\".\" = 3.25 L _. (a?! One-tied test 4. assess whether 2mI Falls within the critical region since Iznh1l> 1.645. it falls within the critical region for rejection of the null hypothesis. therefore. we reject the null hypothesis and conclude that the gasoline aclclitive cloes increase miles per gallon