The College Board reported that the average number of freshman class application

Question

The College Board reported that the average number of freshman class applications to public colleges and universities is 6000. During a recent application/enrollment period, a sample of 32 colleges and universities showed that the sample mean number of freshman class applications was 5812 with a sample standard deviation of 1140.

- State the hypotheses that should be used to test whether the mean number of applications has changed. Answer : Ho: M=6000, Ha:M does not = 6000

- Use the sample results to calculate the value of the test statistic. Answer : t=(xbar-)/(s/n) = (5812-6000)/(1140/32) = -.9328. t=.9328

- With =.05, what is (are) the critical value(s)....Answer: =.05 /2=.025....1-.025=.975=1.96...C.V.=1.96

- What is the statistical conclusion ? Explain. Has the mean number of applications changed ?

Explanation / Answer

The value of test statistics is t=0.9328 Critical value =1.96 Rejection Region: t < -t/2 or t > t/2 That is t<-1.96 or t>1.96 So Here the test statistic value lies in the Acceptance Region. We fail to Reject our Null Hypothesis. That is accept Null Hypothesis. We can conclude that the average number of freshman class applications to public colleges and universities is 6000. That is t<-1.96 or t>1.96 So Here the test statistic value lies in the Acceptance Region. We fail to Reject our Null Hypothesis. That is accept Null Hypothesis. We can conclude that the average number of freshman class applications to public colleges and universities is 6000.

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