Samples of final examination scores for two statistics classes with different in
ID: 3259806 • Letter: S
Question
Samples of final examination scores for two statistics classes with different instructors provided the following results: For instructor "A" the sample size was 12, the sample mean score was 73 and the sample standard deviation was 6. For instructor "B" the sample size was 15, the sample mean score was 77 and the sample standard deviation was 8. At a 5% level of significance, test whether these data are sufficient to conclude that the mean scores for the two classes are the same? What is your conclusion?
Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: 1 = 2
Alternative hypothesis: 1 2
Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the difference between sample means is too big or if it is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a two-sample t-test of the null hypothesis.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = sqrt[(s12/n1) + (s22/n2)]
SE = 2.696
DF = 12 + 15 - 2
D.F = 25
t = [ (x1 - x2) - d ] / SE
t = - 1.48
where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is the size of sample 1, n2 is the size of sample 2, x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between the population means, and SE is the standard error.
Since we have a two-tailed test, the P-value is the probability that a t statistic having 25 degrees of freedom is more extreme than -1.48; that is, less than -1.48 or greater than 1.48.
Thus, the P-value = 0.1697
Interpret results. Since the P-value (0.1697) is greater than the significance level (0.05), we cannot accept the null hypothesis.
From the above test we have sufficient evidence in the favor of the claim that that the mean scores for the two classes are the same.
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