For each test show your complete analysis including the hypo

For each test, show your complete analysis, including: the hypotheses in correct notation, the calculation of the test statistic, the rejection decision using your choice of p-value or critical value approach -- be very precise, and a one-sentence statement that explains the implication of the test result for the issue in question.

The Employment and Training Administration reported the U.S. mean unemployment insurance benefit of $278 per week (The World Almanac 2009). A researcher in the state of California anticipated that sample data would show evidence that the mean weekly unemployment insurance benefit in California was above the national level. A sample of 20 unemployed workers in that state yielded a mean benefit of $293 per week, with a sample standard deviation of $37. Does the data support the research hypothesis or the null hypothesis? Explain.

Solution

Given n=20(small sample, so we use t test), xbar=293, standard deviation=37, & =278. Ho:=278 against H1: not = 278. The table value of t at 0.05 level of significance of (n-1)=(20-1)=19 is 2.09. Then tcal=(xbar-)/[s²/(n-1)]=(293-278)/[(37²/19)]=15/8.4884=1.7671. Here t cal<t tab , so we accept null hypothesus i.e., Ho:=278.