Question

Consider the following competing hypotheses and accompanying sample data drawn independently from normally distributed populations. (Note: the automated question following this one will ask you confidence interval questions for this same data, so jot down your work.)

H0: μ1 − μ2 = 0

HA: μ1 − μ2 ≠ 0

x−1x−1 = 60	x−2x−2 = 56
σ1 = 1.62	σ2 = 10.20
n1 = 25	n2 = 25

Calculate the value of the test statistic. (Negative values should be indicated by a minus sign. Round intermediate calculations to 4 decimal places and final answer to 2 decimal places.)

Test statistic

a-2.	Calculate the p-value of the test statistic. Remember: because this is a two-tailed hypothesis test, you must double your p-value that will be compared with α in the hypothesis test criteria. (Round your answer to 4 decimal places.)

p-value

a-3.	Do you reject the null hypothesis at the 1% level?
	Yes, since the p-value is less than α. No, since the p-value is less than α. Yes, since the p-value is more than α. No, since the p-value is more than α.

b.	Using the critical value approach, can we reject the null hypothesis at the 1% level?
	Yes, since the value of the test statistic is less than the critical value of -1.282. Yes, since the value of the test statistic is less than the critical value of -2.576. No, since the value of the test statistic is not less than the critical value of -1.282. No, since the value of the test statistic is not less than the critical value of -2.576.

Now provide confidence interval information from the previous question. Specifically:

a.    What is the value of the point estimate of the difference between the two population means?

b.    What is the margin of error at 90% confidence?

        (± what value; please provide to 4 decimals; e.g. "3.1234")

c.    With that margin of error, what is the low number in the confidence interval?

d.    With that margin of error, what is the high number in the confidence interval?

Answer 1