Math Problem Statement

You wish to test the following claim ( H a ) at a significance level of α

0.001 . For the context of this problem, μ d

μ 2 − μ 1 where the first data set represents a pre-test and the second data set represents a post-test.

H o : μ d

0

H a : μ d

0

You believe the population of difference scores is normally distributed, but you do not know the standard deviation. You obtain the following sample of data: pre-test post-test 53.6 66.4 51.8 58.9 57.7 60.4 56.2 58.6 55.4 57.5 59.1 60.8 56.4 52.1 49.6 50.1 51.8 55 62 71.9 45.7 50 60.7 72.5 72.6 63.3 46.4 53.5 46 51.5 50.3 53.7 72.6 66.4 49.3 50.3

What is the test statistic for this sample? test statistic = -1.2204 Incorrect (Report answer accurate to 4 decimal places.)

What is the p-value for this sample? p-value = (Report answer accurate to 4 decimal places.)

Solution

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Math Problem Analysis

Mathematical Concepts

Paired t-test
Hypothesis testing
Normal distribution

Formulas

Mean of differences: \bar{d} = \frac{1}{n} \sum_{i=1}^{n} d_i
Standard deviation of differences: s_d = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n} (d_i - \bar{d})^2}
t-statistic for paired t-test: t = \frac{\bar{d}}{s_d / \sqrt{n}}

Theorems

Central Limit Theorem
Student's t-distribution

Suitable Grade Level

Undergraduate (Statistics/Introductory Hypothesis Testing)