**Title: Testing the Mean of Differences in Paired Data****Description:**We are testing the claim about the mean of the differences for a population of paired data at a significance level, α. The assumption is that the samples are random and dependent, and the populations are normally distributed.**Claim:**- Mean difference (μd) = 0- Significance level (α) = 0.01- Sample statistics: Mean difference of the sample ($ \bar{d} $) = 3.1, Standard deviation ($ s_d $) = 8.72, Sample size ($ n $) = 9**Identify the Null and Alternative Hypotheses:**Choose the correct answer from the options below:- A. - $ H_0 $: $ \mu_d < 0 $ - $ H_a $: $ \mu_d \ge 0 $ - B. - $ H_0 $: $ \mu_d \ge 0 $ - $ H_a $: $ \mu_d < 0 $- C. - $ H_0 $: $ \mu_d \neq 0 $ - $ H_a $: $ \mu_d = 0 $- D. (Correct Answer) - $ H_0 $: $ \mu_d = 0 $ - $ H_a $: $ \mu_d \neq 0 $- E. - $ H_0 $: $ \mu_d > 0 $ - $ H_a $: $ \mu_d \le 0 $- F. - $ H_0 $: $ \mu_d \le 0 $ - $ H_a $: $ \mu_d > 0 $**Test Statistic:**- The test statistic is $ t = 1.07 $. - *(Round to two decimal places as needed.)***Critical Value(s):**- The critical value(s) is(are) $ t_0 = \_\_\_ $. - *(Round to two decimal places as needed. Use a comma to separate answers as needed.)*

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Description: **Title: Testing the Mean of Differences in Paired Data****Description:**We are testing the claim about the mean of the differences for a population of paired data at a significance level, α. The assumption is that the samples are random and depende

Solution: From the given information, d-bar=3.1, sd=8.72 and n=9.State the hypotheses. Null hypothesis: H0:µd=0 Alternative hypothesis: Ha: µd≠0 Thus, the correct option is D.Then, the test statistic is Thus, the test statistic is t=1.07.The critical value is Since the test is two-tailed the critical values are –3.36 and 3.36. Thus, the critical values are t0 = –3.36, 3.36.Rejection region: Since the test is two-tailed if the test statistic value (t) less than –3.36 or greater than 3.36, then reject the null hypothesis. Conclusion: Here, the test statistic value is 1.07. This is less than 3.36. By the rejection rule, do not reject the null hypothesis.

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Test the claim below about the mean of the differences for a population of paired data at the level of significance . Assume the samples are random and dependent, and the populations are normally distributed. Claim: Hg = 0; a = 0.01. Sample statistics: d= 3.1, sg = 8.72, n=9 Identify the null and alternative hypotheses. Choose the correct answer below. O B. Ho: Ha 20 Hai Hd 0 OF. Ho: Ha s0 The test statistic is t= 1.07. (Round to two decimal places as needed.) The critical value(s) is(are) to =. (Round to two decimal places as needed. Use a comma to separate answers as needed.)

Test the claim below about the mean of the differences for a population of paired data at the level of significance . Assume the samples are random and dependent, and the populations are normally distributed. Claim: Hg = 0; a = 0.01. Sample statistics: d= 3.1, sg = 8.72, n=9 Identify the null and alternative hypotheses. Choose the correct answer below. O B. Ho: Ha 20 Hai Hd 0 OF. Ho: Ha s0 The test statistic is t= 1.07. (Round to two decimal places as needed.) The critical value(s) is(are) to =. (Round to two decimal places as needed. Use a comma to separate answers as needed.)

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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Topic Video

Question

**Title: Testing the Mean of Differences in Paired Data**

**Description:**

We are testing the claim about the mean of the differences for a population of paired data at a significance level, α. The assumption is that the samples are random and dependent, and the populations are normally distributed.

**Claim:**
- Mean difference (μd) = 0
- Significance level (α) = 0.01
- Sample statistics: Mean difference of the sample ($ \bar{d} $) = 3.1, Standard deviation ($ s_d $) = 8.72, Sample size ($ n $) = 9

**Identify the Null and Alternative Hypotheses:**
Choose the correct answer from the options below:

- A.
- $ H_0 $: $ \mu_d < 0 $
- $ H_a $: $ \mu_d \ge 0 $

- B.
- $ H_0 $: $ \mu_d \ge 0 $
- $ H_a $: $ \mu_d < 0 $

- C.
- $ H_0 $: $ \mu_d \neq 0 $
- $ H_a $: $ \mu_d = 0 $

- D. (Correct Answer)
- $ H_0 $: $ \mu_d = 0 $
- $ H_a $: $ \mu_d \neq 0 $

- E.
- $ H_0 $: $ \mu_d > 0 $
- $ H_a $: $ \mu_d \le 0 $

- F.
- $ H_0 $: $ \mu_d \le 0 $
- $ H_a $: $ \mu_d > 0 $

**Test Statistic:**
- The test statistic is $ t = 1.07 $.
- *(Round to two decimal places as needed.)*

**Critical Value(s):**
- The critical value(s) is(are) $ t_0 = \_\_\_ $.
- *(Round to two decimal places as needed. Use a comma to separate answers as needed.)*

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