A researcher is interested in determining whether a new study program influences

Question

A researcher is interested in determining whether a new study program influences exam scores. To test this, he assigns a sample of n- 30 students to the new program. The data produced a mean of X 39, and s 2.3. The average score in the past semester was 37. 1. a) State the null and alternative hypotheses? (2 points) b) Which type of t-test would you use for this analysis? Why? (1 point) c) Using a 0.05, compute the appropriate t-test to evaluate the hypotheses. (1 point) d) What do you conclude? Include a discussion of the critical value in your answer (1 point)

Explanation / Answer

Given:-

sample mean is X¯=39 and sample standard deviation is s=2.3, and sample size is n = 30.

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: = 37

Ha: 37

This corresponds to a two-tailed test, for which a t-test for one mean, with unknown population standard deviation will be used.

(2) Rejection Region

The significance level is =0.05, and the critical value for a two-tailed test is tc=2.045.

The rejection region for this two-tailed test is R={t:t>2.045}

(3) Test Statistics

The t-statistic is computed as follows:

t = [ (X¯0) / (s/n) ] = [ (3937) / (2.3/30) ] = 4.763

(4) Decision about the null hypothesis

Since it is observed that t=4.763 > tc=2.045, it is then concluded that the null hypothesis is rejected.

P-value : The p-value is p=0, and since p=0<0.05, it is concluded that the null hypothesis is rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population mean is different than 37, at the 0.05 significance level.

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