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 manu- facturer of a national name-brand ketchup asked a sample of shoppers whether they believed that supermarket ketchup was as good as the national brand ketchup. a. 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%. b. 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? c. At a = .05, what is your conclusion? d. Should the national brand ketchup manufacturer be pleased with this conclusion? Explain.

          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 manu- facturer of a national name-brand ketchup asked a sample of shoppers whether they believed that supermarket ketchup was as good as the national brand ketchup.
a. 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%.
b. 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?
c. At a = .05, what is your conclusion?
d. Should the national brand ketchup manufacturer be pleased with this conclusion?
Explain.

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Added by Aaron C.

Essentials of Modern Business Statistics

David R. Anderson, Dennis J.… 5th Edition

Chapter 9

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Solved by Expert Robin Corrigan

09/21/2022

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64). The alternative hypothesis is that the population proportion is not 64% (p ≠ 0.64). Show more…

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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 manu- facturer of a national name-brand ketchup asked a sample of shoppers whether they believed that supermarket ketchup was as good as the national brand ketchup. a. 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%. b. 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? c. At a = .05, what is your conclusion? d. Should the national brand ketchup manufacturer be pleased with this conclusion? Explain.

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Transcript

00:01 Here we are told that a previous study showed that 64 % of supermarket shoppers believe supermarket brands to be as good as national name brands.

00:11 So that's a claim that the proportion.

00:14 And for part a, we are asked to develop hypotheses used to test this claim.

00:24 So the null hypothesis can be that the claim is true, that the population proportion is 0 .64.

00:34 And we want to test whether the proportion is different from 64%.

00:38 So the alternative hypothesis is that the population proportion is not 0 .64.

00:49 And then for part b, we consider a random sample of 100 shoppers, and of these, 52 felt that the supermarket brands were as good as the national brands.

01:06 And so based on this, we are asked for the p value.

01:10 So the first step is to calculate a test statistic.

01:16 This is given by the sample proportion, minus the null -hypothesized.

01:21 Proportion over the square root of the null proportion times 1 minus the null proportion over the sample size.

01:34 So the sample proportion, it's 52 over 100, or 0 .52, and this comes out to minus 2 .5 approximately.

02:08 So the next step is to calculate the p value associated with this test statistic.

02:15 We look at the alternative hypothesis.

02:17 It's a not equals to hypothesis, which means that this is a two -tailed test, and therefore the p value is equal to the probability of getting a number of the probability.

02:24 A test statistic at least as extreme as the one that we got in either the negative or positive directions.

02:45 Let's calculate this using excel...

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