Question

You wish to test the following claim (Ha) about the difference of means for two matched samples at a significance level of α=0.002. For the context of this problem, one data set represents a pre-test and the other data set represents a post-test.

H0: μd = 0
Ha: μd < 0

You believe the population of difference scores is normally distributed, but you do not know the standard deviation. You obtain pre-test and post-test samples for n=40 subjects. The average difference (post - pre) is ¯d=−10.2 with a standard deviation of the differences of sd=29.3

What is the p-value? (Round to 4 decimal places)

Answer 1

The p-value is approximately 0.0845.

Step-by-step explanation:

The p-value can be calculated using the t-distribution for a single population mean. Given that the sample size is 40 with a mean difference (post - pre) of -10.2 and a standard deviation of the differences of 29.3, we can calculate the test statistic as follows:

t = (¯d - μd) / (sd / √n)

Plugging in the values, we get:

t = (-10.2 - 0) / (29.3 / √40) = -1.3961

Using a t-table or t-distribution calculator, we can find the p-value associated with a t-score of -1.3961. The p-value is approximately 0.0845, rounded to 4 decimal places.