You wish to test the following claim (Ho) at a significance level of a = 0.01. For the context of this problem, µd = µ2 – µi where the first data set represents a pre-test and the second data set represe a post-test. Ho: Pd 0 > Prl : ®H You believe the population of difference scores is normally distributed, but you do not know the standar deviation. You obtain pre-test and post-test samples for n = 19 subjects. The average difference (post 17.9 with a standard deviation of the differences of sd = 48.7. pre) is d = - What is the critical value for this test? (Report answer accurate to two decimal places.)

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**Question 2**

You wish to test the following claim (\(H_0\)) at a significance level of \(\alpha = 0.01\). 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.

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

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 \(n = 19\) subjects. The average difference (post - pre) is \(\bar{d} = -17.9\) with a standard deviation of the differences of \(s_d = 48.7\).

**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…

- ( ) 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 accepting the Ho: the mean difference is zero vs. Ha: the mean difference is less than 0.
- ( ) There is not sufficient evidence to warrant accepting the Ho: the mean difference is zero vs. Ha: the mean difference is less than 0.
- ( ) The sample data support rejecting the Ho: the mean difference is zero vs. Ha: the mean difference is less than 0.
- ( ) There is not sufficient sample evidence to support rejecting the Ho: the mean difference is zero vs. Ha: the mean difference is less than 0.
Transcribed Image Text:**Question 2** You wish to test the following claim (\(H_0\)) at a significance level of \(\alpha = 0.01\). 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. \[ H_0: \mu_d = 0 \] \[ H_a: \mu_d < 0 \] 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 \(n = 19\) subjects. The average difference (post - pre) is \(\bar{d} = -17.9\) with a standard deviation of the differences of \(s_d = 48.7\). **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… - ( ) 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 accepting the Ho: the mean difference is zero vs. Ha: the mean difference is less than 0. - ( ) There is not sufficient evidence to warrant accepting the Ho: the mean difference is zero vs. Ha: the mean difference is less than 0. - ( ) The sample data support rejecting the Ho: the mean difference is zero vs. Ha: the mean difference is less than 0. - ( ) There is not sufficient sample evidence to support rejecting the Ho: the mean difference is zero vs. Ha: the mean difference is less than 0.
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