Mr. Santos, a garment store owner, claimed that the brand of sweatpants his customers prefer is Brand A compared to Brand B. He conducted a survey of 100 customers.

Question

Direction: In the following problem, (a) state the null and alternative hypothesis, (b) select and compute the test statistic, (c) determine the critical value and the rejection region, and (d) draw a conclusion. SHOW COMPLETE SOLUTION.

2.    Mr. Santos, a garment store owner, claimed that the brand of sweatpants his customers prefer is Brand A compared to Brand B. He conducted a survey of 100 customers. It was revealed that 55 prefer Brand A and the rest prefer Brand B. At 5% level of significance test the claim of Mr. Santos that the brand of sweatpants his customers prefer is Brand A compared to Brand B.

Answer 1

55 of 100 customers prefer brand A to brand B

alpha = .05

45 of 100 prefer B over A

mean = np = 100(.5) = 50

var = npq = 50(.5) = 25

sd = sqr25 = 5

one tailed test

z critical=1.282

z = (x-mean)/sd = (55-50)/5 = 5/5 = 1

1.282 > 1

fail to reject Ho

Ho: x bar = 50, A and B are equally preferred

Ha: x bar > 50 A is preferred to B