(a) write the claim mathematically and identify Ho and Ha (b) Find the critical
ID: 3218572 • Letter: #
Question
(a) write the claim mathematically and identify Ho and Ha (b) Find the critical value(s) and identify the rejection In a (c) Find the standardized test statistic. (d Decide whether to reject or fail to reject the null hypothesis. sample of 1000 home buyers, you find that 493 home buyers found their real estate agent through a friend At a 0.08, can you reject the claim that 50% of home buyers find their real estate agent through a friend? (a) Which of the following correctly states Ho and Ha? O A. Ho p 0.50 O B. Ho: p 0.50 Ha p20.50 Ha p> 0.50 O D. Ho p20.50 O E. Ho: p 0.50 O F. Ho: 0.50 Ha pExplanation / Answer
Solution:
We want to test whether hypothesis:
H0: p = 0.50
Ha: p 0.50
sample proportion = p = x/n = 493/1000 = 0.493, n=1000
P = 0.50, = 0.08
now calculating statistics
Standard deviation of p = sqrt((P*(1-P))/n) = sqrt((0.50*(1-0.50))/1000) = 0.0158
Test statistic, z = p-0.46/p = (0.493)-0.50/0.0158 = -0.4430
Since this is two tailed test, p-value = 2× P(Z<-0.4430)
= 0.6578
Rejection criteria: Fial to Reject Ho if p-value >
Decision: SInce p-value> , we fail to reject H0. There is not enough evidence to reject the claim that 50% of buyers find their real estate agent through a friend.
Critical value Z/2 = Z0.04 = 1.7507
Rejection criteria : Fail to reject Ho if Z0 is in between (-1.7507, 1.7507)
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