Question

A study was done to investigate what people think is "creepy." Each person in a sample of women and a sample of men were asked to do the following.

Imagine a close friend of yours whose judgment you trust. Now imagine that this friend tells you that she or he just met someone for the first time and tells you that the person was creepy.

The people in the samples were then asked whether they thought the creepy person was more likely to be a male or a female. Of the 1,029 women surveyed, 981 said they thought it was more likely the creepy person was male, and 299 of the 312 men surveyed said they thought it was more likely the creepy person was male.

Is there convincing evidence that the proportion of women who think the creepy person is more likely to be male is different from this proportion for men? For purposes of this exercise, you can assume that the samples are representative of the population of adult women and the population of adult men. Test the appropriate hypotheses using a significance level of 0.05. (Let p1 be the proportion of women who think the creepy person is more likely to be male, and p2 be the proportion of men who think the creepy person is more likely to be male.)

Find the test statistic(z) and P-value. ( Round your test statistic to two decimal places and your P-value to four decimal places.)

z=

p-value=

Answer 1

Given that,
sample one, x1 =981, n1 =1029, p1= x1/n1=0.953
sample two, x2 =299, n2 =312, p2= x2/n2=0.958
finding a p^ value for proportion p^=(x1 + x2 ) / (n1+n2)
p^=0.955
q^ Value For Proportion= 1-p^=0.045
null, Ho: p1 = p2
alternate, H1: p1 != p2
level of significance, α = 0.05
from standard normal table, two tailed z α/2 =1.96
since our test is two-tailed
reject Ho, if zo < -1.96 OR if zo > 1.96
we use test statistic (z) = (p1-p2)/√(p^q^(1/n1+1/n2))
zo =(0.953-0.958)/sqrt((0.955*0.045(1/1029+1/312))
zo =-0.37
| zo | =0.37
critical value
the value of |z α| at los 0.05% is 1.96
we got |zo| =0.37 & | z α | =1.96
make decision
hence value of |zo | < | z α | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != -0.3698 ) = 0.7115
hence value of p0.05 < 0.7115,here we do not reject Ho
ANSWERS
---------------
null, Ho: p1 = p2
alternate, H1: p1 != p2
test statistic: -0.37
critical value: -1.96 , 1.96
decision: do not reject Ho
p-value: 0.7115
we do not have enough evidence to support the claim that the proportion of women who think the creepy person is more likely to be male is different from this proportion for men