Question

A marketing survey involves product recognition in New York and California. Of 558 New Yorkers surveyed, 202 knew the product while 196 out of 614 Californians knew the product. At the 0.05 significance level, test the claim that the recognition rates are higher in New York than the recognition rates in California.

Answer 1

Let

##) for new York

p1→proportion of person knew about products in New York= 202/558= 0.362

Sample size (n1)= 558

##)For California

p2= 196/614=0.319

→p2 proportion of people knew about products in California.

Sample size (n2)= 614

Setting up hypothesis:

Ho: p1= p2

H1: p1>p2

Test statistic t= (p1-p2)/√(p(1-p)(1/n1+1/n2))

p→(n1*p1+n2*p2)/(n1+n2)=0.3396

t=(0.362-0.319)/√((0.3396*0.6604)*(1/558+1/614))= 1.55245

P value= 2*prob(t>1.55245)=0.06

Since p value is greater than level of significance 0.05,we fail to Reject Null hypothesis.

Conclusion→ we have insufficient evidence to support the claim that

recognition rates are higher in New York than the recognition rates in California.

Thanks!