Question

A university student typically spends 15 hours a week on part-time jobs. An officer at a university wants to determine if this amount has changed with the current recession and increase in tuition fees. A sample of 39 students who hold part-time jobs is summarized and has sample mean, = 16.69 and sample standard deviation, s = 7.61.

a) Investigate if there is a reason to believe that there is a change in the average amount of time per week a student spent working pad time at the 1% level of significance

b) What is the rejection region to reject the null hypothesis?

Answer 1

a).here, we will do 1 sample t test for mean.

given data are:-

sample mean () = 16.69

sample sd (s) = 7.61

sample size (n) = 39

level of significance () = 0.01

hypothesis:-

where , is the average time spent in hours by a university student in a week on part-time jobs.

test statistic be:-

degrees of freedom (df) = (n-1) = (39-1) = 38

critical value :-

[ from t distribution table for df = 38, alpha=0.01, both tailed test ]

decision:-

so, we fail to reject the null hypothesis.

conclusion:-

there is not sufficient evidence  to believe that there is a change in the average amount of time per week a student spent working pad time at the 1% level of significance.

b). rejection region:-

reject the null hypothesis if,

or  

diagram:-

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