Question

Christine sells real estate and found that 213 of her homebuyers, 152 found her through a friend. She wished to test a threat against the claim of a national study that 75 % of homebuyers will find their agent through a friend. At a= 0.03 is Christine's result in line with the national study's claim? a) H1 b). c) d)

b). zc or tc c). z or t as appropriate d). interpret the results

Answer 1

a)
Null hypothesis, H0: p = 0.75
Alternative hypo, Ha: p not = 0.75

This is two tailed test

b)

P(z < -2.17) = P(z > 2.17) = 0.015
Rejection region will be on the both sides of the curve because this is two tailed test
Reject H0 if z < -2.17 or z > 2.17

critical values are zc -2.17 and 2.17

c)
pcap = 152/213 = 0.7136

test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.7136 - 0.75)/sqrt(0.75*0.25/213)
z = -1.23

f)
As test statistic > -2.17, fail to reject H0
There is not sufficient evidence to conclude that the proportion is different than 0.75