Question

in a simple random sample of size 78, there were 20 inividuals in the category of interest. It is desired to test H 0:p= ,51 versus H1:p>.51.

i. Compute the sample proportion p.

ii. It is desired to test H0:p= .51 versus H1:p> .51. Compute the test statistic z.

ii. Do you reject H0 at the .01 level?

Answer 1

(A) sample proportion p(hat) = 20/78

= 0.256

(B) given that p(hat) = 0.256, po = 0.51, sample size n= 78

test statistic z =

using z table, check -4.4 in left most column and 0.09 in the top row, then select the intersecting cell, we get

p value = 0.000

p value is less than significance level of 0.01, rejecting the null hypothesis

(C) Reject Ho, there is sufficient evidence to conclude that the proportion is more than 0.51