Part 1 A national newspaper reported that the state with the longest mean life span is Hawaii, where the population mean life span is 73 years. A random sample of 20 obituary notices in the Honolulu Advertizer gave the following information about life span (in years) of Honolulu residents. 72 68 81 93 56 19 78 94 83 84 77 69 85 97 75 71 86 47 66 27 (i) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.) x = yr s = yr (ii) Assuming that life span in Honolulu is approximately normally distributed, does this information indicate that the population mean life span for Honolulu residents is less than 73 years? Use a 10% level of significance. (a) What is the level of significance? ______________________________. State the null and alternate hypotheses. 1) H0: μ = 73 yr; H1: μ > 73 yr 2) H0: μ = 73 yr; H1: μ ≠ 73 yr 3) H0: μ < 73 yr; H1: μ = 73 yr 4) H0: μ = 73 yr; H1: μ < 73 yr 5) H0: μ > 73 yr; H1: μ = 73 yr (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal, since we assume that x has a normal distribution and σ is known. The standard normal, since we assume that x has a normal distribution and σ is unknown. The Student’s t, since we assume that x has a normal distribution and σ is unknown. The Student’s t, since we assume that x has a normal distribution and σ is known. What is the value of the sample test statistic? (Round your answer to three decimal places.) ______________________________. (c) Find the P-value. (Round your answer to four decimal places.) ______________________________. (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α? At the α = 0.10 level, we reject the null hypothesis and conclude the data are statistically significant. At the α = 0.10 level, we reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.10 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the α = 0.10 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (e) Interpret your conclusion in the context of the application. There is sufficient evidence at the 0.10 level to conclude that the population mean life span of Honolulu residents is less than 73 years. There is insufficient evidence at the 0.10 level to conclude that the population mean life span of Honolulu residents is less than 73 years. Part 2 Is the national crime rate really going down? Some sociologists say yes! They say that the reason for the decline in crime rates in the 1980s and 1990s is demographics. It seems that the population is aging, and older people commit fewer crimes. According to the FBI and the Justice Department, 70% of all arrests are of males aged 15 to 34 years†. Suppose you are a sociologist in Rock Springs, Wyoming, and a random sample of police files showed that of 38 arrests last month, 23were of males aged 15 to 34 years. Use a 1% level of significance to test the claim that the population proportion of such arrests in Rock Springs is different from 70%. What is the level of significance? ______________________________. State the null and alternate hypotheses. (Choose one) a)H0: p = 0.7; H1: p > 0.7 b) H0: p = 0.7; H1: p ≠ 0.7 c) H0: p < 0 .7; H1: p = 0.7 d) H0: p = 0 .7; H1: p < 0.7 e) H0: p ≠ 0.7; H1: p = 0.7 3) What sampling distribution will you use? Student's t, since np < 5 and nq < 5. The standard normal, since np > 5 and nq > 5. The Student’s t, since np > 5 and nq > 5. The standard normal, since np < 5 and nq < 5. 4) What is the value of the sample test statistic? (Round your answer to two decimal places.) _________________________. (5) Find the P-value of the test statistic. (Round your answer to four decimal places.) ________________________. (6) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α? a) At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. b) At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. c) At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. d) At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (7) Interpret your conclusion in the context of the application. The is sufficient evidence at the 0.01 level to conclude that the true proportion of arrests of males aged 14 to 34 in Rock Springs differs from 70%. There is insufficient evidence at the 0.01 level to conclude that the true proportion of arrests of males aged 14 to 34 in Rock Springs differs from 70%.