Question

A marketing research firm suspects that a particular product has higher name recognition among college graduates than among high school graduates. A sample from each population is selected, and each asked if they have heard of the product in question. A summary of the sample sizes and number of each group answering yes'' are given below:

College Grads (Pop. 1):High School Grads (Pop. 2):n1=89,n2=97,x1=55x2=49College Grads (Pop. 1):n1=89,x1=55High School Grads (Pop. 2):n2=97,x2=49

The company making the product is willing to increase marketing targeted at high school graduates if the difference between college and high school graduates is more than 5%. Set up a null and alternate hypothesis that can be used to determine if the company should increase marketing for high school graduates.

Note: Use a right-tailed test with p1 for the college proportion and p2 for the high school proportion and state both H0H0 and H1H1 using p1-p2. For 5% enter 0.05

H0:H0:  Use == here.
H1:H1:  

Is there evidence, at an α=0.01α=0.01 level of significance, to support such an increase in marketing? Carry out an appropriate hypothesis test, filling in the information requested.

A. The value of the standardized test statistic:

B. The p-value is

C. Your decision for the hypothesis test:

A. Do Not Reject H1H1 (The company should not increase marketing to high school graduates)
B. Reject H0H0 (The company should increase marketing to high school graduates)
C. Fail to Reject H0H0. (The company should not increase marketing to high school graduates)
D. Reject H1H1 (The company should increase marketing to high school graduates)

Answer 1

null Hypothesis:    Ho:         p1-p2 =		0.00
alternate Hypothesis: Ha:   p1-p2>		0.00

A)

	pop 1	pop 2
x=	55	49
n =	89	97
p̂=x/n=	0.6180	0.5052
estimated prop. diff =p̂1-p̂2    =		0.1128
pooled prop p̂ =(x1+x2)/(n1+n2)=		0.5591
std error Se=√(p̂1*(1-p̂1)*(1/n1+1/n2) =		0.0729
test stat z=(p̂1-p̂2)/Se =		1.550

B)

P value   =

0.0606

(from excel:1*normsdist(-1.55)

c)

C. Fail to Reject H0 (The company should not increase marketing to high school graduates)