You wish to test the following claim (Ho) at a significance level of a = 0.10. For the context of this problem, µd = µ2 – µi where the first data set represents a pre-test and the second data set represents a post-test. Ho: µd = 0 Ha: µd 7 0 (ou 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 = 9 subjects. The average difference (post -

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**Question 4**

You wish to test the following claim (\(H_0\)) at a significance level of \(\alpha = 0.10\). For the context of this problem, \(\mu_d = \mu_2 - \mu_1\) where the first data set represents a pre-test and the second data set represents a post-test.

\[
H_0: \mu_d = 0
\]
\[
H_a: \mu_d \neq 0
\]

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 \(n = 9\) subjects. The average difference (post - pre) is \(\bar{d} = 9\) with a standard deviation of the differences of \(s_d = 44.9\).

What is the critical value for this test? (Report answer accurate to two 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…

- \(\circ\) in the critical region
- \(\circ\) not in the critical region

This test statistic leads to a decision to…

- \(\circ\) reject the null
- \(\circ\) accept the null
- \(\circ\) fail to reject the null

As such, the final conclusion is that…

- \(\circ\) There is sufficient evidence to warrant accepting the \(H_0\): the mean difference is zero vs. \(H_a\): the mean difference is not equal to 0.
- \(\circ\) There is not sufficient evidence to warrant accepting the \(H_0\): the mean difference is zero vs. \(H_a\): the mean difference is not equal to 0.
- \(\circ\) The sample data support rejecting the \(H_0\): the mean difference is zero vs. \(H_a\): the mean difference is not equal to 0.
- \(\circ\) There is not sufficient sample evidence to support rejecting the \(H_0\): the mean difference is zero vs. \(H_a\): the mean difference is not equal to 0.
Transcribed Image Text:**Question 4** You wish to test the following claim (\(H_0\)) at a significance level of \(\alpha = 0.10\). For the context of this problem, \(\mu_d = \mu_2 - \mu_1\) where the first data set represents a pre-test and the second data set represents a post-test. \[ H_0: \mu_d = 0 \] \[ H_a: \mu_d \neq 0 \] 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 \(n = 9\) subjects. The average difference (post - pre) is \(\bar{d} = 9\) with a standard deviation of the differences of \(s_d = 44.9\). What is the critical value for this test? (Report answer accurate to two 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… - \(\circ\) in the critical region - \(\circ\) not in the critical region This test statistic leads to a decision to… - \(\circ\) reject the null - \(\circ\) accept the null - \(\circ\) fail to reject the null As such, the final conclusion is that… - \(\circ\) There is sufficient evidence to warrant accepting the \(H_0\): the mean difference is zero vs. \(H_a\): the mean difference is not equal to 0. - \(\circ\) There is not sufficient evidence to warrant accepting the \(H_0\): the mean difference is zero vs. \(H_a\): the mean difference is not equal to 0. - \(\circ\) The sample data support rejecting the \(H_0\): the mean difference is zero vs. \(H_a\): the mean difference is not equal to 0. - \(\circ\) There is not sufficient sample evidence to support rejecting the \(H_0\): the mean difference is zero vs. \(H_a\): the mean difference is not equal to 0.
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