Question

The belief is that the mean number of hours per week of part-time work of high school seniors in a city is 10.4 hours. Data from a simple random sample of 28 high school seniors indicated that their mean number of part-time work was 11.5 with a standard deviation of 1.3. Test whether these data cast doubt on the current belief. (use α = 0.05)

a. State your null and alternative hypotheses.
b.State the rejection region.

c. Calculate the test statistic.

d. Determine the P-value for your test.

e. State your conclusion for your hypothesis test.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H0 :   = 10.4

Ha : 10.4

df = n - 1 = 27

Critical Value = t /2,df

= t0.025,27

= 2.052

Rejection region = t < -2.052 or t > 2.052

Test statistic (t) =

= ( - ) / s / n

= (11.5 - 10.4) / 1.3 / 28

Test statistic = 4.48

P-value = 0.0001

= 0.05

P-value <

Reject the null hypothesis .

There is sufficient evidence to support the claim.