Question

You wish to test $H_0: \mu_d = 0$ versus $H_1: \mu_d \neq 0$ at a significance level of 0.05. 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. You obtain pre-test and post-test samples for $n_d = 28$ subjects. The average difference (post - pre) is $\bar{x}_d = -5.6$ with a standard deviation of the differences of $s_d = 12.8$. Round your answers to three decimal places. (a). Find the test statistic: (b). Using your answer from part (a), find the p-value: (c). Find the positive critical value for this test: (d). The correct decision is to Select an answer the null hypothesis. (e). There is Select an answer evidence to conclude that the population mean difference is different from 0.

          You wish to test $H_0: \mu_d = 0$ versus $H_1: \mu_d \neq 0$ at a significance level of 0.05. 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. You obtain pre-test and post-test samples for $n_d = 28$ subjects. The average difference (post - pre) is $\bar{x}_d = -5.6$ with a standard deviation of the differences of $s_d = 12.8$.
Round your answers to three decimal places.
(a). Find the test statistic:
(b). Using your answer from part (a), find the p-value:
(c). Find the positive critical value for this test:
(d). The correct decision is to Select an answer the null hypothesis.
(e). There is Select an answer evidence to conclude that the population mean difference is different from 0.

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You wish to test H0: = 0 versus H1: ≠ 0 at a significance level of 0.05. For the context of this problem, = μ2 - μ1 where the first data set represents a pre-test and the second data set represents a post-test. You obtain pre-test and post-test samples for nd = 28 subjects. The average difference (post - pre) is x̅d = -5.6 with a standard deviation of the differences of sd = 12.8.
Round your answers to three decimal places.
(a). Find the test statistic:
(b). Using your answer from part (a), find the p-value:
(c). Find the positive critical value for this test:
(d). The correct decision is to Select an answer the null hypothesis.
(e). There is Select an answer evidence to conclude that the population mean difference is different from 0.

Added by Amanda M.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Kirsty Gledhill

12/14/2023

Step 1

6 - 0}{12.8 / \sqrt{28}} \approx -2.214$$ Show more…

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You wish to test $H_0: \mu_d = 0$ versus $H_1: \mu_d \neq 0$ at a significance level of 0.05. 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. You obtain pre-test and post-test samples for $n_d = 28$ subjects. The average difference (post - pre) is $\bar{x}_d = -5.6$ with a standard deviation of the differences of $s_d = 12.8$. Round your answers to three decimal places. (a). Find the test statistic: (b). Using your answer from part (a), find the p-value: (c). Find the positive critical value for this test: (d). The correct decision is to Select an answer the null hypothesis. (e). There is Select an answer evidence to conclude that the population mean difference is different from 0.

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Transcript

00:01 Okay, so we're testing the null hypothesis that mu d equals zero against the alternative hypothesis that it's less than zero, where d is going to be the post -test score minus the pre -test score.

00:21 And we're doing it at a level alpha equals 0 .02.

00:26 We've got the following sample data.

00:27 Now it's not transcribed very well.

00:29 So what i see written down is pre -test and then straight away post -test.

00:34 And then i see 69 .1, 24 .7, 52 .4, and so on and so on.

00:40 So i've just sort of got a line like this.

00:42 So i can't really tell what's pre -test and what's post -test.

00:44 But i'm going to assume that the pre -test ones are 69 .1 and then the corresponding post -test is 24 .7.

00:52 And then the next pre -test is 52 .4 and then the next post -test is 40 .2.

00:56 So if this is looking right, then that's all good and you don't need to worry.

01:00 If this is the wrong way round for the data, so for example, if these two are the pre -test and post -test scores or something else, then please, could you re -upload the question with like a picture of the data? just because sometimes the way it transcribes makes it quite hard to tell which columns, which numbers are in.

01:19 But so i'm going to be using, assuming this.

01:22 And then we can calculate the difference for these as, so here it would be 24 .7 minus 69 .1, which is minus 44 .4.

01:34 Here it would be minus 12 .2 and so on and so on...

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