Suppose a corrections officer in Washington wants to test the claim that the average time convicted...

Suppose a corrections officer in Washington wants to test the claim that the average time convicted armed burglars with no prior convictions spend time in jail is 104.7 months with a standard deviation of 21 months. He would like to determine if the true mean jail time is actually different from what is claimed, so he collects data for a random sample of 47 such cases from court files and determines that the mean jail time is 110.4 months. The officer conducts a one sample z-test for one mean.

(a) Express the null and alternative hypotheses symbolically. (Be sure to use appropriate symbols).

(b) Determine a 90% confidence interval for the true mean jail time.

(c) Based on the confidence interval, what decision should the police officer make about his hypothesis test? Explain your answer.

Solutions

Expert Solution

H0: = 104.7

Ha: 104.7

90% confidence interval for is

- Z/2 * / sqrt(n) < < + Z/2 * / sqrt(n)

110.4 - 1.645 * 21 / sqrt(47) < < 110.4 + 1.645 * 21 / sqrt(47)

105.36 < < 115.44

90% CI is ( 105.36 , 115.44 )

Since confidence interval does not contain mean 104.7 , we have sufficient evidence to suppot

the claim that the true mean jail time is actually different from 104.7 months.

orchestra answered 1 year ago

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