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

H_A: μ₁ − μ₂ ≠ 0

x−1x−1 = 74	x−2x−2 = 65
σ1 = 1.57	σ2 = 14.10
n1 = 19	n2 = 19

a-1.	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 5% level?
	No, since the p-value is more than α. No, since the p-value is less than α. Yes, since the p-value is more than α. Yes, since the p-value is less than α.

b.	Using the critical value approach, can we reject the null hypothesis at the 5% level?
	No, since the value of the test statistic is not less than the critical value of-1.645. No, since the value of the test statistic is not less than the critical value of -1.96. Yes, since the value of the test statistic is less than the critical value of -1.645. Yes, since the value of the test statistic is less than the critical value of -1.96.

Answer 1

Hope this will help you. Thank you :)