Independent random samples are selected from two populations and are used to test the hypothesis H0:(μ1−μ2)=0H0:(μ1−μ2)=0 against the alternative Ha:(μ1−μ2)≠0.Ha:(μ1−μ2)≠0. An ­analysis of 233 observations from population 1 and 312 from ­population 2 yielded a p-value of .115.

a). Interpret the results of the test.
b). If the alternative hypothesis had been Ha:(μ1−μ2)<0,Ha:(μ1−μ2)<0, how would the p-value change? Interpret the p-value for this one-tailed test.

a. We do not have enough evidence to conclude that the two means differ.

b. There is no difference in the population means.

Step-by-step explanation:

a) Results of the test:

Having p - value to be very high, we have strong evidence of not rejecting H o and hence,

We do not have enough evidence to conclude that the two means differ.

b) For a one tailed test,

p - value = 0.115/2 = 0.0575

Interpretation: p - value is the probability of getting the difference as small as obtained in the sample, given that the null hypothesis is true i.e. there is no difference in the population means.