Question

Read each problem carefully and clearly show all work. Indicate calculator functions used (ie T-Test, 2-SampTTest, etc) as well as calculator entries State your conclusions in terms of the context of the problem

2) All students at Big-Huge College must take an assessment test before they can attend their first math class. A random group of 9 students were given the math placement test and their scores were recorded. They were then allowed to retake the exact same test 4 times and their final score was recorded. The mean of the differences is 6.4 and the standard deviation of the differences is 4.16. Does taking the test 4 times change the average placement score? Use a 0.05 level of significance. Assume the population of differences is normal. Note: the differences are in the right most column of the table below. Student Score 1st time Score 4th try Difference: 4th try – 1st try 1 32 38 6 2 45 49 4 3 33 35 2 4 28 44 16 5 26 32 6 6 27 36 9 7 32 35 3 8 20 25 5 9 21 28 7

Clearly label the 6 step approach

Answer 1

This is a Paired t-test.

The hypothesis being tested is:

H0: µd = 0

Ha: µd ≠ 0

xd = 6.4

sd = 4.16

n = 9

The test statistic, t = xd/sd/√n = 6.4/4.16/√9 = 1.2

The p-value is 0.2645.

Since the p-value (0.2645) is greater than the significance level (0.05), we cannot reject the null hypothesis.

Therefore, we cannot conclude that taking the test 4 times changes the average placement score.

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