Question

1. 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 28 seniors indicated that their mean number of parttime work was 12.5 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.)Sketch the rejection region.

c.) Calculate the test statistic. Plot this value in your sketch in part b.

d.) Determine the P-value for your test.

e.) State your conclusions clearly in complete sentences.

Answer 1

a)

Ho :   µ =   10.7
Ha :   µ ╪   10.7

b)

degree of freedom=   DF=n-1=   27
      

      
critical t value, t* =    ±   2.052

rejection region:t < -2.052 or t > 2.052

c) Standard Error , SE = s/√n =   1.3000   / √    28   =   0.2457      
t-test statistic= (x̅ - µ )/SE = (   12.500   -   10.7   ) /    0.2457   =   7.327

d)

p-Value   =   0.000000

f) Decision:   p-value<α, Reject null hypothesis   
Conclusion: There is enough evidence to conclude that mean number of hours per week of part-time work of high school seniors in a city is not 10.7 hours