You wish to test the following claim ( H a ) at a significance level of α = 0.02 . 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 74.9 107.6 77.2 80.3 70.1 62.7 84.3 64.4 68.1 97.4 36.9 42.6 What is the critical value for this test? (Report answer accurate to three decimal places.) critical value = What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = The test statistic is... in the critical region not in the critical region 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 greater than 0. There is not sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is greater than 0. The sample data support the claim that the mean difference of post-test from pre-test is greater than 0. There is not sufficient sample evidence to support the claim that the mean difference of post-test from pre-test is greater than 0

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

You wish to test the following claim (
H
a
) at a significance level of
α
=
0.02
. 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
74.9 107.6
77.2 80.3
70.1 62.7
84.3 64.4
68.1 97.4
36.9 42.6

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

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

The test statistic is...
in the critical region
not in the critical region

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