# Testing of Hypothesis : Students t test

One sample t test, Independent sample t test, Z test for population proportion . See attached file for full problem description.

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25. Consider the following hypothesis test:

H :µ ≥ 45

º

H :µ < 45

A sample of 36 is used. Identity the p-value and state your conclusion for each of the following sample results. Use a = .01

a. _

x = 44 and s = 5.2

b. _

x = 43 and s = 4.6

c. _ = 46 and s = 5.0

x

Answer

The test Statistic is given by

Rejection criteria: Reject the null hypothesis, if the calculated value of t is less than the critical value of t with n-1 d.f.

Or if the p value is less than the significance level 0.01

The critical value = -2.4377

Given that n = 36

The results are summarized in the table below

s Test statistic P value conclusion

44 5.2 -1.1538 0.1282 Accept H0

43 4.6 -2.6087 0.0066 Reject H0

46 5.0 1.2 0.8809 Accept H0

27. The Employment and Training Administration reported the U.S. mean unemployment insurance benefit of $238 per week. A researcher in the state of Virginia anticipated that sample data would show evidence that the mean weekly unemployment insurance benefit in Virginia was below the national level.

A. Develop appropriate hypotheses such that rejection of H will support the researcher's contention º

B. For a sample of 100 individuals, the sample mean weekly unemployment insurance benefit was $231 with a sample standard deviation of $80. What is the p-value.

C. At a =0.05, what is your conclusion?

D. Repeat the preceding hypothesis test using the critical value approach.

Answer

The null hypothesis under consideration is

H0: The Virginia mean unemployment insurance benefit = $238 per week

H1: The Virginia mean unemployment insurance benefit < $238 per week

B. The ...

#### Solution Summary

Testing of Hypothesis: One sample t test, Independent sample t test, Z test for population proportion are calculated.