Question

A researcher wants to test the claim that convicted burglars spend an average of 18.7 months in jail. She takes a random sample of 11 such cases from court files and finds that x̅ =20.6 months and s=7.8 months. Test the claim that μ = 18.7 months at the 0.05 significance level.

Answer 1

Solution

Given,

μ = 18.7 claim about population mean

n = 11 sample size

x̅ =20.6 sample mean

s = 7.8 sample SD

= 0.05 significance level

Since the population SD is unknown , we use the t test.

Hypothesis can be written as

H0: μ = 18.7 vs H1 : μ 18.7

The test statistic t is

t =

= (20.6 - 18.7)/(7.8/11)

= 0.808

Now , sign in H1 indicates that the test is Two Tailed. So the critical values are  

i.e.

i.e   

i.e   

Since , ∣t∣=0.808≤ t_c​=2.228, so we fail to reject H0: μ = 18.7

So we support the the claim that μ = 18.7 .The mean is not significantly different than 18.7