The university wants to promote the graduates of its honors program by proving t

Question

The university wants to promote the graduates of its honors program by proving that the mean GPA of these graduates exceeds 3.50 even though at present it is stated that the GPA is 3.50 or below. A sample of 36 university honors program students is taken and is found to have a mean GPA equal to 3.60. The population standard deviation is assumed to equal 0.40 a) To establish whether the mean GPA exceeds 3.5, the appropriate hypotheses: b) At a 5% significance level, the critical value is: c) The value of the test statistics is: What decision should be made? d) The p-value is: What decision should be made?

Explanation / Answer

Answers to the question, below:

a.

The hypothesis can set up as:

Ho:Mu<=3.5
Ha:Mu>3.5

b. the critical value at 5% significance level is Z = 1.645

c. test statistic = Z

= (X-Mu)/(Sigma/sqrt(n))

= (3.6-3.5)/(.4/sqrt(36))

= 1.5

Decision: Since test statistics is lesser than critical value of 1.645 it lies in the non critical range, thus we do not reject Ho. We conclude that it doesn't exceed 3.5

d. p-value at Z = 1.5 is 1-.9332 = .0668. Again alpha = .05<.0668 so our point lies outside the critical region and we do not reject Ho. We conclude that it doesn't exceed 3.5

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