(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.

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.

 1.      It is claimed that 70% of SHS students in a certain district have internet at home. A survey among 1500 SHS students in that district revealed that 1025 have internet at home. Use 0.05 level of significance

 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

.7 x 1500 = 1050 student expected to have internet at home

1250 have internet at home

1250/1500 = 125/150 = 5/6 = .8333...

alpha = .05

two tailed test

mean = np = 1500(.7) = 1050

var = npq = 1050(.3) = 315

sd = sqr315 =17.75

us z tables or z calculator to find z critical = 1.98

or empirical rule for less precise z critical = 2.0

z= (x- mean)/sd = (1250-1050)/17.75 = 200/17.75 = 11.27

11.27> 2.0 or 1.98

reject Ho: mean=.70,

Ha: mean > 70%