Question

17A national newspaper reported that the state with the longest mean life span is Hawaii, where the population

mean life span is 78 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 78 years? Use a 5% level of significance.

(a) What is the level of significance?

 (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.)

19A random sample of 30 binomial trials resulted in 12 successes. Test the claim that the population proportion of successes does not equal 0.50. Use a level of significance of 0.05.

(a) Can a normal distribution be used for the p̂ distribution? Explain. 

Yes, np and nq are both less than 5.

Yes, np and nq are both greater than 5.  

No, np is greater than 5, but nq is less than 5.

No, np and nq are both less than 5.

No, nq is greater than 5, but np is less than 5.

(c) Compute p̂. 

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