Question

You wish to test the following claim ( H a ) at a significance level of α = 0.01 . H o : μ 1 = μ 2 H a : μ 1 < μ 2 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 n 1 = 24 with a mean of M 1 = 71.2 and a standard deviation of S D 1 = 11.3 from the first population. You obtain a sample of size n 2 = 15 with a mean of M 2 = 73.6 and a standard deviation of S D 2 = 9.2 from the second population. 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? (Report answer accurate to four decimal places.) p-value = The p-value is... less than (or equal to) α greater than α 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.

Answer 1

The test statistic t = (M1 - M2)/sqrt(s1^2/n1 + s2^2/n2)

                          = (71.2 - 73.6)/sqrt((11.3)^2/24 + (9.2)^2/15)

                          = -0.725

DF = (s1^2/n1 + s2^2/n2)^2/((s1^2/n1)^2/(n1 - 1) + (s2^2/n2)^2/(n2 - 1))

     = ((11.3)^2/24 + (9.2)^2/15)^2/(((11.3)^2/24)^2/23 + ((9.2)^2/15)^2/14)

     = 34

P-value = P(T < -0.725)

           = 0.2367

The p-value is greater than . This test statistic leads to a decision to fail to reject the null.

There is sufficient evidence to warrant rejection of the claim that the first population mean is less than the second population mean.