Question

Dr. Harper roe wants to check the claim that convicted burglars in gularte county spend an average of 18.7 months in jail. he takes a random sample of 11 cases from the gularte county court files and finds that a mean of 20.5 months with a standard deviation of 7.9 months is the time burglars spend in jail test the claim that the mean time spent is 18.7 months at the 0.05 significance level.

A) Claim, null hypo, alternative hypo

B Test to be used, what is the p-value?

C classical approach test statistic, and the critical value?

D What is the conclusion

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :   = 18.7

H_a :    18.7

Test statistic = t

= ( - ) / s / n

= (18.7 - 20.5) / 7.9 / 11

= -0.76

df = 10

P-value = 0.4648

= 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z _0.025 = +/-1.96

Test statistic < critical value

Fail to reject the null hypothesis .