Question

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.

Answer 1

a)

H0: = 104.7

Ha: 104.7

b)

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 )

c)

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.