Question

A random sample of 200 freshman and 100 seniors at Ferris High School are asked whether they agree with a plan to excuse upper class students (juniors and seniors) a half hour early while keeping underclass students (freshmen and sophomores) in school for the last half hour. Of the students sampled, 160 freshmen opposed the plan and 20 seniors opposed the plan.

Is there a difference (5% level of significance) between the proportion of freshmen who oppose the plan and the proportion of seniors who oppose it? Do a complete test showing all the parts.

Answer 1

Null hypotheses H_o : There is no difference between the proportion of freshman who opposes plan and the proportion of seniors who oppose it .

Alternative hypotheses H₁ : There is a difference between the proportion of freshman who opposes plan and the proportion of seniors who oppose it.

Test statistic = Z = ( p1 - p2 ) / (( p*(1-p) ( (1/n1) + (1/n2) ))^0.5

p1 = 160/200 = 0.8

p2 = 20 / 100 =0.2

p = ( 0.8*n₁ + 0.2* n₂ ) / (n₁ + n₂ )

n₁ = 200 and n₂ = 100

p = (0.8 * 200 + 0.2*100 )/ ( 300) = 0.6

Z= ( 0.8 - 0.2 ) / ( 0.6 * 0.4 * ( (1/200) + (1/100)))^0.5

Z = 10

tabulated Z = Z_0.025 = 1.96

Since, Calculated Z = 10 > 1.96 (tabulated Z) , we reject Ho at 5 % level of significance and conclude that there is a difference between the proportion of freshman who opposes plan and the proportion of seniors who oppose it.