Question

For each test, show the 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.

The Employment and Training Administration reported the U.S. mean unemployment insurance benefit of $278 per week (The World Almanac 2019). 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 $290 per week, with a sample standard deviation of $37. Does the data support the research hypothesis (i.e., alternative) at the default level of significance? Explain.

Answer 1

Let the mean weekly unemployment insurance benefit in California be denoted by

Here we are to test

The given data is summarized as :

Sample size(n)=20

Sample mean()=290

Sample SD(s)=37

The test statistic is obtained as

The test statistic follows t distribution with df 19

The p-value is obatined as 0.081628

As the p-value is more than 0.05, we fail to reject the null hypothesis at 5% level of significance and thus conclude that the reseracher hypothesis is not supported by the data at 5% level of significance.

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