Question

Table 6.25 gives a sample of grades on the first two quizzes 1in an introductory statistics course. We are interested in testing whether the mean grade grade TABLE 6.25Are grades higher on the second quiz? First Quiz on the second quiz is significantly higher than the on the first quiz mean 72 9556 87 80 98 74 85 77 62 Second Quiz 78 96 72 89 80 95 86 87 82 75 Complete the test if we assume that the grades from the first quiz come from a random sample of 10 students in the course and the grades on the second quiz come from a different separate random sample of 10 students in the course. a) The Null and Alternative Hypothesis b) The test statistic c) The p-value d) A sketch including the appropriate curve as well as labeling the test statistic and p-value. e) A decision (Reject or Do not reject) f The concluding statement in context 1. Now conduct the test if we assume that the grades recorded for the first quiz and the second 2. order. (So the first student got a 72 on the first are from the quiz same 10 students in the same quiz and a 78 on the second quiz.) a) The Null and Alternative Hypothesis b) The test statistic c) The p-value d) A sketch including the appropriate curve as e) A decision (Reject or Do not reject) f The concluding statement in context. well as labeling the test statistic and p-value. Why are the results so different? Which is a better way to collect the data to answer the 3. question of whether grades are higher on the second quiz?

Answer 1

Terminal Console > first=c(72,95,56,87,80,98,74,85,77,62) second c(78,96,72,89,80,95,86,87,82,75) #a) Nul1 hypothesis Ho: mu first > #Alternative hypothesis Ha: mu first < mu second #b) #since this is 1 - 1 comparision we need to perform 2 sample paired t test t.test(first,second,alternative = "less",mu =0) = mu second > Welch Two Sample t-test first and second data: t = -1.0931, df alternative hypothesis: true difference in means is less than 0 95 percent confidence interval: 14.763, p-value 0.1459 -Inf 3.269341 sample estimates: mean of X mean of y 78,6 84.0 #C ) p value #e)since p value of the test is not less than 0.05 we cannot Reject Ho > #e) Hence we can conclude that there is no as shown above is 0. 1459 > significant improvement on the score of the 2nd quiz

d)For d plot a normal distribution curve with lower limit -inf and upper limit as +3.269 as shown below

3 9 -6 3 6

Above test performed in R. You can use any tool to do the same.

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