In: Statistics and Probability
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?
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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