Brownies Wingman\'s (a food market chain) has developed a new store-brand browni

Question

Brownies Wingman's (a food market chain) has developed a new store-brand brownie to Before they start selling the mix they want to compare how well people like their brownies to brownies made from a popular national brand mix. In order to see if there was any difference in consumer opinion, Wingman's asked 124 shoppers to participate in a taste test. Each was given a brownie to try. Subjects were not told which kind of brownie they got-that was determined randomly, 58% of the 62 shoppers who tasted a W Egan's brownie said they liked it well enough to buy the mix, compared to 66% of the others who said they would be willing to buy the national brand. Does this result indicate that consumer interest in the Wingman's mix is lower than for the national brand?

Explanation / Answer

proportion of wegman=p1=0.58 , sample size=n1=62

proportion of national brand=p2=0.66, sample size=n2=62

here we use z-test to test the different in proportion

null hypothesis H0:p1=p2 and alternate hypothesis H1:p1<p2

z=(p1-p2)/SE(p1-p2)==(p1-p2)/sqrt((p1(1-p1)/n1)+(p2(1-p2)/n2))

=(0.58-0.66)/sqrt((0.58*(1-0.58)/62)+(0.66*(1-0.66)/62))=-0.92

one-tailed critical z(0.05)=1.645 is more than absolute value of calculated z=0.92, so we fail to reject H0 .Therefore we accept H0 p1=p2 and conclude that consuemer interest in wegman is not lower than the national brand

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