Question

Use the following information to answer questions 13-17: The belief is that the mean number of hours per week of part-time work of high school seniors in a city is 10.7 hours. Data from a simple random sample of 24 high school seniors indicated that their mean number of part-time work was 11.6 with a standard deviation of 1.4. Test whether these data cast doubt on the current belief. (use α = 0.05) Part a: State your null and alternative hypotheses. Part b: State the rejection region. Part c: Calculate the test statistic. Part d: Determine the P-value for your test. Part e: State your conclusion for your hypothesis test.

Answer 1

Solution :

= 10.7

=11.6

S =1.4

n = 24

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :    = 10.7

H_a :     10.7

Test statistic = t

= ( - ) / S / n

= (11.6-10.7) /1.4 / 24

= 3.149

Test statistic = t = 3.149

P-value =0.0045

= 0.05  

P-value <

0.0045 < 0.05

Reject the null hypothesis .

There is sufficient evidence to claim that the population mean μ is different than 10.7, at the 0.05 significance level.