You wish to test the following claim (Ha) at a significance level of α=0.001. For the context of this problem, μd=μ2−μ1 where the first data set represents a pre-test and the second data set represents a post-test. Ho: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 the following sample of data: pre-test post-test 59.8 42.4 42.5 37 48.2 12.7 56.5 42.8 49.3 26.8 60.6 58.5 61.3 43.4 56 40.6 57.5 39 60.1 56.6 40 29.8 52.6 47.8 51.5 39 55.6 34.6 55.1 39.2 What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is... less than (or equal to) αα greater than αα This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is not equal to 0. There is not sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is not equal to 0. The sample data support the claim that the mean difference of post-test from pre-test is not equal to 0. There is not sufficient sample evidence to support the claim that the mean difference of post-test from pre-test is not equal to 0.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.3: Special Probability Density Functions

Problem 8E

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Question

You wish to test the following claim (Ha) at a significance level of α=0.001. For the context of this problem, μd=μ2−μ1 where the first data set represents a pre-test and the second data set represents a post-test.

Ho: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 the following sample of data:

pre-test	post-test
59.8	42.4
42.5	37
48.2	12.7
56.5	42.8
49.3	26.8
60.6	58.5
61.3	43.4
56	40.6
57.5	39
60.1	56.6
40	29.8
52.6	47.8
51.5	39
55.6	34.6
55.1	39.2

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

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

The p-value is...

less than (or equal to) αα
greater than αα

This test statistic leads to a decision to...

reject the null
accept the null
fail to reject the null

As such, the final conclusion is that...

There is sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is not equal to 0.
There is not sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is not equal to 0.
The sample data support the claim that the mean difference of post-test from pre-test is not equal to 0.
There is not sufficient sample evidence to support the claim that the mean difference of post-test from pre-test is not equal to 0.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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