Answered: A study showed that 66% of supermarket…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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$A study showed that 66% 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 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 66%.** - $ H_0: p $ is **equal to 0.66** ✅ - $ H_a: p $ is **not equal to 0.66** ✅ **b. If a sample of 100 shoppers showed 53 stating that the supermarket brand was as good as the national brand, what is the p-value (to 4 decimals)?** - **0.0005** ❌ **c. At $ \alpha = .05 $, what is your conclusion?** - p-value is **less than or equal to 0.05, reject** $ H_0 $ ✅ **d. Should the national brand ketchup manufacturer be pleased with this conclusion?** - **Yes** ✅. Since $ \bar{p} = $. **0005** ❌, it indicates that **fewer** ✅ than **.05** % of the shoppers believe the supermarket brand is as good as the name brand.$

Transcribed Image Text:A study showed that 66% 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 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 66%.** - $ H_0: p $ is **equal to 0.66** ✅ - $ H_a: p $ is **not equal to 0.66** ✅ **b. If a sample of 100 shoppers showed 53 stating that the supermarket brand was as good as the national brand, what is the p-value (to 4 decimals)?** - **0.0005** ❌ **c. At $ \alpha = .05 $, what is your conclusion?** - p-value is **less than or equal to 0.05, reject** $ H_0 $ ✅ **d. Should the national brand ketchup manufacturer be pleased with this conclusion?** - **Yes** ✅. Since $ \bar{p} = $. **0005** ❌, it indicates that **fewer** ✅ than **.05** % of the shoppers believe the supermarket brand is as good as the name brand.

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