Question

The time required to start a business, defined as the number of days needed to complete the procedures to legally operate a business, in 20 developed countries and 20 emerging countries is included in the accompanying table. Assuming that the population variances for developed countries and emerging countries are not equal, is there evidence of a difference in the mean time required to start a business between developed countries and emerging countries? (Use α = 0.05.) Compare these results to those from the test for equal means when the variances are assumed to be equal.

Let be the mean time required to start a business in developed countries and let μ2 be the mean time required to start a business in emerging countries. What are the null and alternative hypotheses?
a. H0 : μ1 ≠ μ2
H1 : μ1=μ2
b. H0 : μ1 ≥ μ2
H1 : μ1<μ2
c. H0 : μ1 ≤ μ2
H1 : μ1>μ2
d. H0 : μ1 = μ2
H1 : μ1≠μ2

Answer 1

The correct null hypothesis (H0) for testing the difference in mean times to start a business between developed and emerging countries is that the means are equal (μ1 = μ2), and the alternative hypothesis (Ha) is that they are not equal (μ1 ≠ μ2). Therefore, the correct option is D.

Step-by-step explanation:

When comparing the mean time required to start a business between developed and emerging countries with the assumption that the population variances are not equal, we conduct a two-sample t-test with unequal variances. The correct null and alternative hypotheses for testing if there is a difference in the mean times between the two groups are:

• H0: μ1 = μ2 (There is no difference in the mean times to start a business between the two groups.)
• Ha: μ1 ≠ μ2 (There is a difference in the mean times to start a business between the two groups.)

This corresponds to the option d. H0: μ1 = μ2 and H1: μ1 ≠ μ2. The alternative hypothesis is two-tailed as we are testing for any possible difference, not just in one direction.