A national newspaper reported that the state with the longest mean life span is Hawaii, where the population mean life span is 79 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 79 years? Use a 5% level of significance. (a) What is the level of significance? State the null and alternate hypotheses. a: μ < 79 yr; H1: μ = 79 yr b: μ = 79 yr; H1: μ ≠ 79 yr c: μ > 79 yr; H1: μ = 79 yr d: μ = 79 yr; H1: μ < 79 yr e: μ = 79 yr; H1: μ > 79 yr (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. a. The standard normal, since we assume that x has a normal distribution and σ is unknown. b. The Student's t, since we assume that x has a normal distribution and σ is unknown. c. The standard normal, since we assume that x has a normal distribution and σ is known. d. 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) Estimate the P-value.a. P-value > 0.250 a. 0.100 < P-value < 0.250 a. 0.050 < P-value < 0.100 a. 0.010 < P-value < 0.050 a. P-value < 0.010
A national newspaper reported that the state with the longest mean life span is Hawaii, where the population mean life span is 79 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
(a) What is the level of significance?
State the null and alternate hypotheses.
a: μ < 79 yr; H1: μ = 79 yr
b: μ = 79 yr; H1: μ ≠ 79 yr
c: μ > 79 yr; H1: μ = 79 yr
d: μ = 79 yr; H1: μ < 79 yr
e: μ = 79 yr; H1: μ > 79 yr
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
a. The standard normal, since we assume that x has a normal distribution and σ is unknown.
b. The Student's t, since we assume that x has a normal distribution and σ is unknown.
c. The standard normal, since we assume that x has a normal distribution and σ is known.
d. 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) Estimate the P-value.
a. P-value > 0.250
a. 0.100 < P-value < 0.250
a. 0.050 < P-value < 0.100
a. 0.010 < P-value < 0.050
a. P-value < 0.010
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