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=86,n2=85,x1=52x2=37 The company making the product is willing to increase marketing targeted at high school graduates if the difference between the two groups is at least 5%. Is there evidence, at an α=0.081 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:

Note: For the next part, your answer should use interval notation. An answer of the form (−∞,a) is expressed (-infty, a), an answer of the form (b,∞) is expressed (b, infty), and an answer of the form (−∞,a)∪(b,∞) is expressed (-infty, a)U(b, infty).

B. The rejection region for the standardized test statistic:

C. The p-value is

D. Your decision for the hypothesis test:

A. Do Not Reject H1.

B. Reject H1.

C. Reject H0.

D. Do Not Reject H0

Answer 1

using excel>addin>phstat>z test for difference

we have

Z Test for Differences in Two Proportions
Data
Hypothesized Difference	0.05
Level of Significance	0.081
Group 1
Number of Items of Interest	52
Sample Size	86
Group 2
Number of Items of Interest	37
Sample Size	85
Intermediate Calculations
Group 1 Proportion	0.604651163
Group 2 Proportion	0.435294118
Difference in Two Proportions	0.169357045
Average Proportion	0.5205
Z Test Statistic	1.5621
Lower-Tail Test
Lower Critical Value	-1.3984
p-Value	0.9409
Do not reject the null hypothesis

A. The value of the standardized test statistic:1.5621

B. The rejection region for the standardized test statistic: (−∞,1.5621)

C. The p-value is 0.9409

D. Your decision for the hypothesis test:

D. Do Not Reject H0