For a comparison of two study guides for a mathematics course, 14 student volunt

Question

For a comparison of two study guides for a mathematics course, 14 student volunteers were found. They were randomly assigned, 7 to study guide A, and 7 to study guide B. Following a two-day period of independent study, the students were examined on the material. The students received the following scores (out of 100): Use a permutation test to test the null hypothesis that the distributions of scores are the same for each study guide, against the two-sided alternative that the distributions are different. How many possible ways are there to randomly allocate the 14 students into two groups of 7 students? Compute the difference in sample means, bar A - bar B, as the test statistic. How many arrangements of the data would lead to an absolute value of the computed test statistic as great or greater than the absolute value of the test statistic you calculated in the previous question? Note that you don't have to list all possible arrangements in order to answer this. Examine the data carefully and use the trick that was shown in class (also on pages 8-9 of the typed notes) for the permutation problem. Suppose that after examining all the possible arrangements, it is found that the absolute value of the difference in means for 10 of the arrangements (including the real one that you observed) are greater than or equal to the absolute value of the computed test statistic. What is the two-sided p-value for the permutation test?

Explanation / Answer

1) number of ways to distribute 14 students into 2 classes =14!/(7!*7!) =3432

2)

hence Abar-Bbar =89.57143-72 =17.57143

3)as there are two values in B (80 and 82) which are higher then minimum value of A(77).

hence by replacing them we can have 2 values of where Abar-Bbar would be higher then test stat.

Now the same combination of A if, it will be in B and all values of B in A, then 2 more combinations will be there where absolute value will be higher then test statistics,

hence number of ways =4

A B 93 69 87 62 94 80 77 72 91 82 94 71 91 68 mean 89.57143 72

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.