Statistic Questions?

Question

In a poll of 212 prison wardens, 98 said that tattoos are a sign of trouble. Find the sample proportion who think tattoos are a sign of trouble.


Using the problem above, to test the claim that less than half of all prison wardens think tattoos are a sign of trouble, write the null and alternative hypothesis.


Using the problem above, find the value of the test statistic.


Find the P-value for the test statistic you just found.


Test the claim at the .01 significance level and state whether the null hypothesis is rejected or not.
State the conclusion for the claim that less than half of prison wardens dislike tattoos.

Answer 1

The proportion of wardens who think tattoos are a sign of trouble is the number of wardens who think tattoos are a sign of trouble divided by the sample size, 98/212 = 0.4623.

 

Hº: The proportion of wardens who feel that tattoos are a sign of trouble is ≥ 0.5

Hª: The proportion of wardens who feel that tattoos are a sign of trouble is < 0.5

 

z = (p - P)/sqrt(P(1-P)/n)

 

where p is the sample proportion and P is the proportion in the claim.

 

z = (.4623-.5)/sqrt(.5(1-.5)/212) = -.0377/.0343 = -1.1

 

P(Z<-1.1) = 0.13567

 

Since 0.13 > 0.01 (α), the sample data fails to reject the null hypothesis.

 

Alternatively we can calculate a critical z for α=0.01.

This is a one tailed test so we find z for p-value .01 which is -2.326.

Since the sample z score (-1.1) is not in the region of rejection (<-2.326), the sample data fails to reject the null hypothesis.