(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

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

Ho: p = 0.7

Ha: p != 0.7

phat = 1025/1500 = 0.68

z = (0.68 - 0.7)/sqrt(0.7 * 0.3/1500) = -1.69

critical region for alpha = 0.05 are z < -1.96 or z > 1.96,

since z not in critical region, do not reject Ho.

 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.

if neither is preferred then proportion preferring brand A is 0.5.

Ho: p = 0.5

Ha: p > 0.5

phat = 55/100 = 0.55

z = (0.55 - 0.5)/sqrt(0.5*0.5/100) = 1

rejection region for alpha = 0.05 and right sided test is z > 1.645

because z not in rejection region do not reject Ho