Question

A national newspaper reported that the state with the longest mean life span is Hawaii, where the population mean life span is 74 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 74 years? Use a 5% level of significance.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: μ = 74 yr; H₁: μ > 74 yrH₀: μ = 74 yr; H₁: μ < 74 yr    H₀: μ = 74 yr; H₁: μ ≠ 74 yrH₀: μ > 74 yr; H₁: μ = 74 yrH₀: μ < 74 yr; H₁: μ = 74 yr

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The Student's t, since we assume that x has a normal distribution and σ is unknown.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 known.

What is the value of the sample test statistic? (Round your answer to three decimal places.)


(c) Estimate the P-value.

P-value > 0.2500.100 < P-value < 0.250    0.050 < P-value < 0.1000.010 < P-value < 0.050P-value < 0.010

Sketch the sampling distribution and show the area corresponding to the P-value.

(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 = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.    At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the α = 0.05 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 0.05 level to conclude that the population mean life span of Honolulu residents is less than 74 years.There is insufficient evidence at the 0.05 level to conclude that the population mean life span of Honolulu residents is less than 74 years.    

Answer 1

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