Question

Consider the following competing hypotheses: Use Table 2.

H₀: μ_D ≥ 0; H_A: μ_D < 0

d-bar = −2.3, s_D = 7.5, n = 23

The following results are obtained using matched samples from two normally distributed populations:

a.	At the 10% significance level, find the critical value(s). (Negative value should be indicated by a minus sign. Round intermediate calculations to 4 decimal places and final answer to 2 decimal places.)

Critical value

b.	Calculate the value of the test statistic under the assumption that the difference is normally distributed. (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.)

Test statistic

c.

What is the conclusion to the hypothesis test?

	Do not reject H0 since the value of the test statistic is not less than the critical value.
	Reject H0 since the value of the test statistic is not less than the critical value.
	Do not reject H0 since the value of the test statistic is less than the critical value.
	Reject H0 since the value of the test statistic is less than the critical value.

Answer 1

Given that, d-bar = -2.3, S_D = 7.5, n = 23

The null and the alternative hypotheses are,

a) t-critical value at significance level of 0.10 with degrees of freedom = 23 - 1= 22 is, t^* = -1.321

=> Critical value = -1.32

b) Test statistic is,

=> Test statistic = -1.47

c) Since, test statistic = -1.47 < -1.32, we reject H₀

Answer: Reject H0 since the value of the test statistic is less than the critical value.