(12 points) A researcher is interested in comparing student exam scores in a cla

Question

(12 points) A researcher is interested in comparing student exam scores in a class where the students learn from a traditional textbook and one where they learn using only a CD-ROM. Two classes consisting of randomly selected students are used in the same semester. The researcher is curious as to whether the scores differ, but does not have any prior idea of which method is better. You may assume that these data are normal and have equal variances. Select the appropriate statistical test, state the null and alternative hypotheses that are appropriate, test the data, and draw a conclusion. Do the two methods differ? Hand calculate this test. Final exam scores (in percents): Standard textbook: 98, 87, 85, 82, 81, 80, 80 75, 72, 70, 70, 70, 68, 62 CD-ROM: 99, 85, 85, 81, 80, 80, 79, 79, 74, 73, 72, 64, 63, 61, 60

Explanation / Answer

In statistics, hypothesis testing is a confirmatory analysis of statistical data to make yes or no decisions. A hypothesis test analyse the results of null hypothesis and alternative hypothesis of a population. The final decisions are usually made by conducting null hypothesis test. If p value is small, H0 will be rejected and large p-values will not allow to reject H0. P-value, T-score and test result can be calculated using Hypothesis Testing based on population mean.

We define µb to be the mean number of scores of students studying from standard textbook and

µw to be the mean number of scores of students studying from CD - ROM. The hypotheses are:

So µb = (98+87+85+82+81+80+80+75+72+70+70+70+68+62)/14 = 1080/14 = 77.14

and µw = (99+85+85+81+80+80+79+79+74+73+72+64+63+61+60)/15 = 1135/15 = 75.66

H0 : µb = µw
Ha : µb > µw

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