A study by Consumer Reports showed that 64% of supermarket shoppers believe supe
ID: 3170243 • Letter: A
Question
A study by Consumer Reports showed that 64% of supermarket shoppers believe supermarket brands to be as good as national name brands. To investigate whether this result applies to its own product, the manufacturer of national name-brand ketchup asked a sample of shoppers whether they believed that supermarket ketchup was as good as the national brand ketchup. 1) Formulate the hypotheses that could be used to determine whether the percentage of supermarket shoppers who believe that the supermarket ketchup was as good as the national brand ketchup differed from 64%. 2) If a sample of 100 shoppers showed 52 stating that the supermarket brand was as good as the national brand, what is the p-value? 3) At alpha = 0.05. what is your conclusion? 4) Should the national brand ketchup manufacturer be pleased with this conclusion? Explain.Explanation / Answer
1. H0 (Null): p = 0.64
H1 (Alternate): p < 0.64
Alternate hypothesis by national brand states that less than 64% believe supermarket ketchup better than national brand ketchup.
2. p0 = 0.64, p^ = 52/100 = 0.52
z = (p^ -p0) / sqrt of (p0 *(1-p0)/n)
= 0.12 / sqrt of (0.52*0.48)/100 = 2.401
p-value = 0.008
3) since p <0.05, reject H0. We can reject Null and reject the fact that 64% shoppers believe supermarket brand to be as good as national brand
4) National brand should be pleased with the conclusion that the default belief (null hypothesis) is wrong. No significant evidence is available that shoppers prefer supermarket brand to be as good as national brand
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