Hypothesis Test for Difference in Population Means (o Unknown) You wish to test the following claim (Ha) at a significance level of a = 0.05. Ho:41 = 42 T11 > Irt : "H You believe both populations are normally distributed, but you do not know the standard deviations for either. We will assume that the population variances are not equal. You obtain a sample of size n = 10 with a mean of M1 = 74.2 and a standard deviation of SD = 12.8 from the first population. You obtain a sample of size n2 = 26 with a mean of M2 = 79.3 and a standard deviation of SD2 = 20.3 from the second population. l What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p-value for this sample? For this calculation, use the conservative under-estimate for the degrees of freedom. The degrees of freedom is the minimum of ng - 1 and n2 - 1. (Report answer accurate to four decimal places.) p-value - The p-value is... less than (or equal to) a O greater than a This test statistic leads to a decision to... O reject the null accept the null O fail to reject the null
Hypothesis Test for Difference in Population Means (o Unknown) You wish to test the following claim (Ha) at a significance level of a = 0.05. Ho:41 = 42 T11 > Irt : "H You believe both populations are normally distributed, but you do not know the standard deviations for either. We will assume that the population variances are not equal. You obtain a sample of size n = 10 with a mean of M1 = 74.2 and a standard deviation of SD = 12.8 from the first population. You obtain a sample of size n2 = 26 with a mean of M2 = 79.3 and a standard deviation of SD2 = 20.3 from the second population. l What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p-value for this sample? For this calculation, use the conservative under-estimate for the degrees of freedom. The degrees of freedom is the minimum of ng - 1 and n2 - 1. (Report answer accurate to four decimal places.) p-value - The p-value is... less than (or equal to) a O greater than a This test statistic leads to a decision to... O reject the null accept the null O fail to reject the null
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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![**Hypothesis Test for Difference in Population Means (\( \sigma \) Unknown)**
You wish to test the following claim (\( H_a \)) at a significance level of \( \alpha = 0.05 \).
\[ H_0: \mu_1 = \mu_2 \]
\[ H_a: \mu_1 < \mu_2 \]
You believe both populations are normally distributed, but you do not know the standard deviations for either. We will assume that the population variances are not equal.
You obtain a sample of size \( n_1 = 10 \) with a mean of \( M_1 = 74.2 \) and a standard deviation of \( SD_1 = 12.8 \) from the first population. You obtain a sample of size \( n_2 = 26 \) with a mean of \( M_2 = 79.3 \) and a standard deviation of \( SD_2 = 20.3 \) from the second population.
**What is the test statistic for this sample? (Report answer accurate to three decimal places.)**
\[ \text{test statistic} = \_\_\_\_ \]
**What is the p-value for this sample? For this calculation, use the conservative under-estimate for the degrees of freedom. The degrees of freedom is the minimum of \( n_1 - 1 \) and \( n_2 - 1 \). (Report answer accurate to four decimal places.)**
\[ \text{p-value} = \_\_\_\_ \]
**The p-value is…**
- [ ] less than (or equal to) \( \alpha \)
- [ ] greater than \( \alpha \)
**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 rejection of the claim that the first population mean is less than the second population mean.
- [ ] There is not sufficient evidence to warrant rejection of the claim that the first population mean is less than the second population mean.
- [ ] The sample data support the claim that the first population mean is less than the second population mean.
- [ ] There is not sufficient sample evidence to support the claim that the first population mean is less than the second population mean](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4c34f4d9-e916-4e51-bbe7-df3a13f5e09c%2Fdee80c79-7cb5-40aa-92ba-3fe5880653e3%2F377ejcq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Hypothesis Test for Difference in Population Means (\( \sigma \) Unknown)**
You wish to test the following claim (\( H_a \)) at a significance level of \( \alpha = 0.05 \).
\[ H_0: \mu_1 = \mu_2 \]
\[ H_a: \mu_1 < \mu_2 \]
You believe both populations are normally distributed, but you do not know the standard deviations for either. We will assume that the population variances are not equal.
You obtain a sample of size \( n_1 = 10 \) with a mean of \( M_1 = 74.2 \) and a standard deviation of \( SD_1 = 12.8 \) from the first population. You obtain a sample of size \( n_2 = 26 \) with a mean of \( M_2 = 79.3 \) and a standard deviation of \( SD_2 = 20.3 \) from the second population.
**What is the test statistic for this sample? (Report answer accurate to three decimal places.)**
\[ \text{test statistic} = \_\_\_\_ \]
**What is the p-value for this sample? For this calculation, use the conservative under-estimate for the degrees of freedom. The degrees of freedom is the minimum of \( n_1 - 1 \) and \( n_2 - 1 \). (Report answer accurate to four decimal places.)**
\[ \text{p-value} = \_\_\_\_ \]
**The p-value is…**
- [ ] less than (or equal to) \( \alpha \)
- [ ] greater than \( \alpha \)
**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 rejection of the claim that the first population mean is less than the second population mean.
- [ ] There is not sufficient evidence to warrant rejection of the claim that the first population mean is less than the second population mean.
- [ ] The sample data support the claim that the first population mean is less than the second population mean.
- [ ] There is not sufficient sample evidence to support the claim that the first population mean is less than the second population mean
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