Question

Consider the following competing hypotheses: (You may find it useful to reference the appropriate table: z table or t table) H0: μD ≥ 0; HA: μD < 0 d¯ = −4.0, sD = 5.8, n = 20 The following results are obtained using matched samples from two normally distributed populations: a-1. Calculate the value of the test statistic, assuming that the sample difference is normally distributed. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) a-2. Find the p-value. 0.025 p value < 0.05 0.05 p value < 0.10 p value 0.10 p value < 0.01 0.01 p value < 0.025 b. At the 5% significance level, what is the conclusion to the hypothesis test? Do not reject H0 since the p value is greater than the significance level. Reject H0 since the p value is greater than the significance level. Do not reject H0 since the p value is less than the significance level. Reject H0 since the p value is less than the significance level. c. Interpret the results at α = 0.05. We can cannot conclude that the mean difference differs from zero. We conclude that the mean difference differs from zero. We cannot conclude that that the mean difference is less than zero. We conclude that the mean difference is less than zero.

Answer 1

(a-1) test statistic =

setting the given values, we get

(a-2) using excel function T.DIST(x,df)

setting x = -3.08 and degree of freedom = n-1

= 20-1= 19

So, p value = T.DIST(-3.08,19) = 0.0031

p value is less than 0.01

(B) it is clear that the p value is less than 0.05 significance level, this means that the result is significant and we can reject the null hypothesis at 0.05 significance level

so, we will reject Ho

option D

Reject H0 since the p value is less than the significance level. c. Interpret the results at α = 0.05

(C) Yes, we can conclude that the mean difference is less than 0 because the result is significant. We have already the null hypothesis, this means the mean difference is less than 0

option D

We conclude that the mean difference is less than zero.