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A Test involving the Population Mean (Large Samples) Exercises Answers to the even-numbered exercises are at the back of the book. 1. The Public Health Service publishes the Annual Data Tabula- tions, Continuous Air Monitoring Projects, which recently indi- cated that a large midwestern city had an annual mean level of sulfur dioxide of 0.12 (concentration in parts per million), To change this concentration, many steel mills and other manu- facturers installed antipollution equipment. Plans are to make about 36 random checks during the year to determine if there has been a change in the sulfur dioxide level. The 0.05 level is to be used. a. State both the null hypothesis and the alternate hypothesis. b. What is the level of significance? c. What is the appropriate test statistic? Give its formula, d. Show the decision rule in the form of a diagram. e. Thirty-six random checks were made throughout the year. It was found that the sample mean was 0.10 and the sam- ple standard deviation 0.03. At the 0.05 level, does this ev- idence indicate that there has been a change in the sulfur dioxide level in the city? f. Compute the p-value. 2. During the past several years, frequent checks were made of the spending patterns of citizens returning from a vacation of 21 days or less to countries in Europe. Results indicated that trav- elers spent an average of $1,010 on items such as souvenirs, meals, film, and gifts. A new survey is to be conducted to de- termine if there has been a change in the average amount spent. The 0.01 level is to be used. a. State the null hypothesis and the alternate hypothesis in the forms Ho and He. b. State the decision rule. c. A survey of 50 travelers has a sample mean of $1,090. The standard deviation of the sample was $300. At the 0.01 level, is there evidence that there has been a change in the mean amount spent abroad, or is the increase of $80 prob- ably due to chance? d. Compute the p-value. 3. A West Coast study of a very large population showed that the mean time devoted to volunteer political and civic activities was 32 minutes per month, with a population standard devia- tion of 4.5 minutes. A smaller group of 49 similar individuals who lived in the South reported a mean of 34 minutes per month. Is this difference possibly due to sampling error, or does it represent a significant difference at the 0.0$ level? 4. A local manufacturer of doors for use in home construction is attempting to determine if the average height of adult males in