Question

You wish to test the following claim ( H a ) at a significance level of ? = 0.002 . H o : ? 1 = ? 2 H a : ? 1 ? ? 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 = 17 with a mean of ¯ x 1 = 69.8 and a standard deviation of s 1 = 12.3 from the first population. You obtain a sample of size n 2 = 28 with a mean of ¯ x 2 = 74.7 and a standard deviation of s 2 = 20.8 from the second population. What is the test statistic for this sample? test statistic = Round to 3 decimal places. What is the p-value for this sample? For this calculation, use . p-value = Use Technology Round to 4 decimal places. The p-value is... less than (or equal to) ? greater than ? 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 not equal to the second population mean. There is not sufficient evidence to warrant rejection of the claim that the first population mean is not equal to the second population mean. The sample data support the claim that the first population mean is not equal to the second population mean. There is not sufficient sample evidence to support the claim that the first population mean is not equal to the second population mean.

Answer 1

Ans:

Assumption:population variances are not equal.

Test statistic:

t=(69.8-74.7)/sqrt((12.3^2/17)+(20.8^2/28))

t=-0.993

df=17-1=16

(we use smaller of n₁-1 and n_2-1 as df for conservative case in case of unequal variances)

p-value=tdist(0.993,16,2)=0.3355

*(if df=43 is used,then p-value=0.3263)

p-value is greater than alpha

This test statistic leads to a decision to fail to reject the null hypothesis.

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