Question

In: Statistics and Probability

You wish to test the following claim (H1H1) at a significance level of α=0.002α=0.002. Ho:μ1=μ2Ho:μ1=μ2 H1:μ1≠μ2H1:μ1≠μ2...

You wish to test the following claim (H1H1) at a significance level of α=0.002α=0.002.

Ho:μ1=μ2Ho:μ1=μ2
H1:μ1≠μ2H1:μ1≠μ2

You believe both populations are normally distributed, but you do not know the standard deviations for either. However, you also have no reason to believe the variances of the two populations are not equal. You obtain a sample of size n1=19n1=19 with a mean of M1=77.6M1=77.6 and a standard deviation of SD1=20.7SD1=20.7 from the first population. You obtain a sample of size n2=20n2=20 with a mean of M2=72.1M2=72.1 and a standard deviation of SD2=8.7SD2=8.7 from the second population.

2a. What is the critical value for this test? (Report answer accurate to three decimal places.)
critical value =

2b. What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

2c. The test statistic is...

A. in the critical region

B. not in the critical region

2d. This test statistic leads to a decision to...

A. reject the null

B. accept the null

C. fail to reject the null

2e. As such, the final conclusion is that...

A. There is sufficient evidence to warrant rejection of the claim that the first population mean is not equal to the second population mean.

B. There is not sufficient evidence to warrant rejection of the claim that the first population mean is not equal to the second population mean.

C. The sample data support the claim that the first population mean is not equal to the second population mean.

D. There is not sufficient sample evidence to support the claim that the first population mean is not equal to the second population mean.

Expert Solution

Solution

2a. What is the critical value for this test? (Report answer accurate to three decimal places.)
critical value =3.468

2b. What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic

2c. The test statistic is...

B. not in the critical region

2d. This test statistic leads to a decision to...

C. fail to reject the null

2e. As such, the final conclusion is that..

D. There is not sufficient sample evidence to support the claim that the first population mean is not equal to the second population mean.

orchestra answered 1 year ago

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