A researcher, under the guise of a participant, joined two “singles clubs” to te

ID: 3061241 • Letter: A

Question

A researcher, under the guise of a participant, joined two “singles clubs” to test the advertised superiority of one over the other. He observed several patrons from each club and noted their dating status (single or dating) after one month in the club. The data are as follows: Club A Club B Number Observed 126 157 Number “Dating” 41 74 Test the hypothesis that Club B is more successful in initiating acquaintances than Club A. Use = .05, 2-tailed. (Hint: I need the z and whether to reject or retain the null hypothesis)

Explanation / Answer

Given data is as follows;

Club A

Club B

Number Observed

n= 126

M = 157

Number Dating

d1 = 41

d2 = 74

Proportion

p1= d1/n = 41/126 =

p2 = d2/n = 41/126 =

Pooled Proportion

p = (d1+d2)/(n+m) = (41+74)/(126+157) =

Set up the hypothesis as follows;

H0: Both Clubs have the same popularity Vs HA: Club B is more successful in advertising.

Z = (p1-p2)/pq(1/n+1/m) ~ N(0,1)

Z = (0.325397-0.471338)/(0.40636*0.59364*(1/126+1/157)

Z =

|Z| = 2