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 21 high school seniors indicated that their mean number of part-time work was 11.4 with a standard deviation of 1.2. 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 :

= 10.4

=11.4

S =1.2

n = 21

a ) This is the two tailed test .

The null and alternative hypothesis is ,

H0 :    = 10.4

Ha :     10.4

b ) The critical value = +/- 2.08

c ) Test statistic = t

= ( - ) / S / n

= (11.4 - 10.4) / 1.2 / 21

= 3.819

Test statistic = t = 3.819

d ) P-value =0.0011

= 0.05  

P-value <

0.0011 < 0.05

e ) Reject the null hypothesis .

There is sufficient evidence to suggest that