A marketing research firm suspects that a particular product

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):n1=97, x1=67

High School Grads (Pop. 2): n2=94, x2=48

Is there evidence, at an ?=0.059 level of significance, to support the claim of higher name recognition among college graduates? Carry out an appropriate hypothesis test, filling in the information requested.

A. The value of the standardized test statistic:

B. The p-value is:

Solution

Test For Significance of Difference Of Proportion
Null Hypothesis, There Is No Significance between them Ho: p1 < p2
Alternate Hypothesis, There Is Significance between them H1: p1 > p2
A)
Test Statistic
Sample 1 : X1 =67, n1 =97, P1= X1/n1=0.6907
Sample 2 : X2 =48, n2 =94, P2= X2/n2=0.5106
Finding a P^ value For Proportion P^=(X1 + X2 ) / (n1+n2)
P^=0.6021
Q^ Value For Proportion= 1-P^=0.3979
we use Test Statistic (Z) =   (P1-P2)/?(P^Q^(1/n1+1/n2))
Zo =(0.691-0.5106)/Sqrt((0.602*0.3979(1/97+1/94))
Zo =2.5421
| Zo | =2.5421
Critical Value
The Value of |Z ?| at LOS 0.059% is 1.563
We got |Zo| =2.542 & | Z ? | =1.563
Make Decision
Hence Value of | Zo | > | Z ?| and Here we Reject Ho
B)
P-Value: Right Tail -Ha : ( P > 2.5421 ) = 0.00551
Hence Value of P0.059 > 0.00551,Here we Reject Ho