Assume that the differences are normally distributed. Observation Xi Yi 1 42.9 46.4 2 51.1 52.9 3 47.6 49.2 4 45.5 50.2 5 51.5 52.7 6 48.3 52.2 7 50.5 51.6 8 43.3 45.8 (a) Determine di = Xi - Yi for each pair of data. Observation 1 2 3 4 5 6 7 8 di -3.5 -1.8 -1.6 -4.7 -1.2 -3.9 -1.1 -2.5 (Type integers or decimals.) Compute d̄ and sd. d̄ = -2.538 (Round to three decimal places as needed.) sd = 1.349 (Round to three decimal places as needed.) (c) Test if μd < 0 at the α = 0.05 level of significance. What are the correct null and alternative hypotheses? C. H0: μd = 0 H1: μd < 0 P-value = 0.001 (Round to three decimal places as needed.) Choose the correct conclusion below. A. Do not reject the null hypothesis. There is sufficient evidence that μd < 0 at the α = 0.05 level of significance. B. Reject the null hypothesis. There is insufficient evidence that μd < 0 at the α = 0.05 level of significance. C. Do not reject the null hypothesis. There is insufficient evidence that μd < 0 at the α = 0.05 level of significance. D. Reject the null hypothesis. There is sufficient evidence that μd < 0 at the α = 0.05 level of significance. (d) Compute a 95% confidence interval about the population mean difference μd. The lower bound is __?__. The upper bound is __?__. (Round to two decimal places as needed.)
Added by Tara M.
Step 1
Since the sample size is small (n = 8), we will use the t-distribution. The degrees of freedom are n - 1 = 8 - 1 = 7. For a 95% confidence interval and 7 degrees of freedom, the critical value (t*) is approximately 2.365. Show more…
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Assume that the differences are normally distributed. Complete parts (a) through (d) below: Observation 42.3 47.2 43.6 46.4 47.9 45.6 48.2 49.6 45.5 46.4 45.7 50.5 50.4 45.7 49.4 49.7 (a) Determine di = Xi - Yi for each pair of data Observation (Type integers or decimals:) (b) Compute d and Sd. d = (Round to three decimal places as needed:) Sd = (Round to three decimal places as needed) (c) Test if μd < 0 at the α = 0.05 level of significance. What are the correct null and alternative hypotheses? A. Ho: μd < 0 H1: μd > 0 B. Ho: μd = 0 H1: μd < 0 C. Ho: μd < 0 H1: μd = 0 D. Ho: μd > 0 H1: μd < 0 P-value (Round to three decimal places as needed) Choose the correct conclusion below: Reject the null hypothesis. There is insufficient evidence that μd < 0 at the α = 0.05 level of significance. Do not reject the null hypothesis. There is sufficient evidence that μd < 0 at the α = 0.05 level of significance. Do not reject the null hypothesis. There is insufficient evidence that μd < 0 at the α = 0.05 level of significance. Reject the null hypothesis. There is sufficient evidence that μd < 0 at the α = 0.05 level of significance. (d) Compute 95% confidence interval about the population mean difference μd
Keondre P.
Madhur L.
Question 1 For a one sample t-Test: If the 95% Confidence interval of the difference does include the value of zero, the which of the following is correct? a. The statistical results are statistically significant and we reject the p-value b. We reject the p-value and the population estimate c. We retain the point estimate and the results are statistically significant d. We reject the alternative hypothesis and retain the null hypothesis Question 2 For a one sample t-Test: If the 95% Confidence interval of the difference does not include the value of zero, the which of the following is correct? a. We retain the point estimate and the results are statistically significant b. We reject the null hypothesis and retain the alternative hypothesis c. The statistical results are statistically significant and we reject the p-value d. We reject the p-value and the population estimate Question 3 For an independent samples t-Test: If the 95% Confidence interval of the difference does not include the value of zero, the which of the following is correct? a. The statistical results are statistically significant and we reject the p-value b. We reject the null hypothesis and retain the alternative hypothesis c. We reject the p-value and the population estimate d. We retain the point estimate and the results are statistically significant Question 4 For an independent samples t-Test: If the 95% Confidence interval of the difference does include the value of zero, the which of the following is correct? a. The statistical results are statistically significant and we reject the p-value b. We reject the alternative hypothesis and retain the null hypothesis c. We retain the point estimate and the results are statistically significant d. We reject the p-value and the population estimate
Sri K.
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