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You wish to test the following claim (\(H_a\)) at a significance level of \(\alpha = 0.10\). \[ H_0: \mu_1 = \mu_2 \\ H_a: \mu_1 > \mu_2 \] You believe both populations are normally distributed, but you do not know the standard deviations for either. And you have no reason to believe the variances of the two populations are equal. You obtain a sample of size \(n_1 = 13\) with a mean of \(\bar{x}_1 = 80.6\) and a standard deviation of \(s_1 = 19.9\) from the first population. You obtain a sample of size \(n_2 = 28\) with a mean of \(\bar{x}_2 = 75.9\) and a standard deviation of \(s_2 = 20.5\) from the second population. a. What is the test statistic for this sample? \[ \text{test statistic} = \underline{\hspace{3cm}} \] Round to 3 decimal places. b. What is the p-value for this sample? For this calculation, use. \[ \text{p-value} = \underline{\hspace{3cm}} \] Use Technology Round to 4 decimal places. c. The p-value is… - [ ] less than (or equal to) \(\alpha\) - [ ] greater than \(\alpha\) d. This test statistic leads to a decision to… - [ ] reject the null - [ ] accept the null - [ ] fail to reject the null

You wish to test the following claim (\(H_a\)) at a significance level of \(\alpha = 0.10\). \[ H_0: \mu_1 = \mu_2 \\ H_a: \mu_1 > \mu_2 \] You believe both populations are normally distributed, but you do not know the standard deviations for either. And you have no reason to believe the variances of the two populations are equal. You obtain a sample of size \(n_1 = 13\) with a mean of \(\bar{x}_1 = 80.6\) and a standard deviation of \(s_1 = 19.9\) from the first population. You obtain a sample of size \(n_2 = 28\) with a mean of \(\bar{x}_2 = 75.9\) and a standard deviation of \(s_2 = 20.5\) from the second population. a. What is the test statistic for this sample? \[ \text{test statistic} = \underline{\hspace{3cm}} \] Round to 3 decimal places. b. What is the p-value for this sample? For this calculation, use. \[ \text{p-value} = \underline{\hspace{3cm}} \] Use Technology Round to 4 decimal places. c. The p-value is… - [ ] less than (or equal to) \(\alpha\) - [ ] greater than \(\alpha\) d. This test statistic leads to a decision to… - [ ] reject the null - [ ] accept the null - [ ] fail to reject the null

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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You wish to test the following claim (\(H_a\)) at a significance level of \(\alpha = 0.10\). \[ H_0: \mu_1 = \mu_2 \\ H_a: \mu_1 > \mu_2 \] You believe both populations are normally distributed, but you do not know the standard deviations for either. And you have no reason to believe the variances of the two populations are equal. You obtain a sample of size \(n_1 = 13\) with a mean of \(\bar{x}_1 = 80.6\) and a standard deviation of \(s_1 = 19.9\) from the first population. You obtain a sample of size \(n_2 = 28\) with a mean of \(\bar{x}_2 = 75.9\) and a standard deviation of \(s_2 = 20.5\) from the second population. a. What is the test statistic for this sample? \[ \text{test statistic} = \underline{\hspace{3cm}} \] Round to 3 decimal places. b. What is the p-value for this sample? For this calculation, use. \[ \text{p-value} = \underline{\hspace{3cm}} \] Use Technology Round to 4 decimal places. c. The p-value is… - [ ] less than (or equal to) \(\alpha\) - [ ] greater than \(\alpha\) d. This test statistic leads to a decision to… - [ ] reject the null - [ ] accept the null - [ ] fail to reject the null
Transcribed Image Text:You wish to test the following claim (\(H_a\)) at a significance level of \(\alpha = 0.10\). \[ H_0: \mu_1 = \mu_2 \\ H_a: \mu_1 > \mu_2 \] You believe both populations are normally distributed, but you do not know the standard deviations for either. And you have no reason to believe the variances of the two populations are equal. You obtain a sample of size \(n_1 = 13\) with a mean of \(\bar{x}_1 = 80.6\) and a standard deviation of \(s_1 = 19.9\) from the first population. You obtain a sample of size \(n_2 = 28\) with a mean of \(\bar{x}_2 = 75.9\) and a standard deviation of \(s_2 = 20.5\) from the second population. a. What is the test statistic for this sample? \[ \text{test statistic} = \underline{\hspace{3cm}} \] Round to 3 decimal places. b. What is the p-value for this sample? For this calculation, use. \[ \text{p-value} = \underline{\hspace{3cm}} \] Use Technology Round to 4 decimal places. c. The p-value is… - [ ] less than (or equal to) \(\alpha\) - [ ] greater than \(\alpha\) d. This test statistic leads to a decision to… - [ ] reject the null - [ ] accept the null - [ ] fail to reject the null
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