Question

Consider the following competing hypotheses: (You may find it useful to reference the appropriate table: z table or t table)


H₀: μ_D ≥ 0; H_A: μ_D < 0

d¯d¯  = −3.2, s_D = 6.0, n = 23

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

The statistical software output for this problem is :

Test statistics = -2.56

P-value < 0.01

Reject H₀ since the p value is less than the significance level.

We conclude that the mean difference is less than zero.