A study showed that 62% 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 is less than 62%. Ho: P = 0.62 HP 0.62 Ho: p2 0.62 H: P<0.62 Ho: P < 0.62 H₂: P2 0.62 Ho: P>0.62 H: Ps 0.62 Ho: P ≤ 0.62 H:p> 0.62 (b) If a sample of 100 shoppers showed 49 stating that the supermarket rand was as good as the national brand, what is the p-value? Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value= (c) At a = 0.05, what is your conclusion? Do not reject Ho. There is insufficient evidence to conclude that the percentage of supermarket shoppers who believe that supermarket ketchup is as good as the national brand ketchup is less than 62%. Do not reject Ho. There is sufficient evidence to conclude that the percentage of supermarket shoppers who believe that supermarket ketchup is as good as the national brand ketchup is less than 62%. Reject Ho. There is sufficient evidence to conclude that the percentage of supermarket shoppers who believe that supermarket ketchup is as good as the national brand ketchup is less than 62%. Reject Ho. There is insufficient evidence to conclude that the percentage of supermarket shoppers who believe that supermarket ketchup is as good as the national brand ketchup is less than 62% A m 1 cricut -

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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$### Hypothesis Testing for Supermarket Ketchup Preference A study showed that 62% 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) Hypothesis Formulation Formulate the hypotheses that could be used to determine whether the percentage of supermarket shoppers who believe that the supermarket ketchup is as good as the national brand ketchup is less than 62%. 1. $ \mathrm{H_0: p = 0.62} $ 2. $ \mathrm{H_1: p \neq 0.62} $ 3. $ \mathrm{H_1: p > 0.62} $ 4. $ \mathrm{H_0: p > 0.62} $ 5. $ \mathrm{H_1: p \geq 0.62} $ 6. $ \mathrm{H_0: p \leq 0.62} $ 7. $ \mathrm{H_0: p < 0.62} $ 8. $ \mathrm{H_1: p < 0.62} $ 9. $ \mathrm{H_0: p \geq 0.62} $ #### (b) Sample and Test Statistic If a sample of 100 shoppers showed 49 stating that the supermarket brand was as good as the national brand, what is the p-value? Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to four decimal places.) \[ \text{p-value } = \underline{\ \ \ \ \ \ \ } \] #### (c) Conclusion at $ \alpha = 0.05 $ At $ \alpha = 0.05 $, what is your conclusion? - Do not reject $ \mathrm{H_0} $. There is insufficient evidence to conclude that the percentage of supermarket shoppers who believe that supermarket ketchup is as good as the national brand ketchup is less than 62%. - Do not reject $ \mathrm{H_1} $. There is sufficient evidence to conclude that the percentage of supermarket shoppers who believe that supermarket ketchup is as good as the national brand ketchup$

Transcribed Image Text:### Hypothesis Testing for Supermarket Ketchup Preference A study showed that 62% 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) Hypothesis Formulation Formulate the hypotheses that could be used to determine whether the percentage of supermarket shoppers who believe that the supermarket ketchup is as good as the national brand ketchup is less than 62%. 1. $ \mathrm{H_0: p = 0.62} $ 2. $ \mathrm{H_1: p \neq 0.62} $ 3. $ \mathrm{H_1: p > 0.62} $ 4. $ \mathrm{H_0: p > 0.62} $ 5. $ \mathrm{H_1: p \geq 0.62} $ 6. $ \mathrm{H_0: p \leq 0.62} $ 7. $ \mathrm{H_0: p < 0.62} $ 8. $ \mathrm{H_1: p < 0.62} $ 9. $ \mathrm{H_0: p \geq 0.62} $ #### (b) Sample and Test Statistic If a sample of 100 shoppers showed 49 stating that the supermarket brand was as good as the national brand, what is the p-value? Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to four decimal places.) \[ \text{p-value } = \underline{\ \ \ \ \ \ \ } \] #### (c) Conclusion at $ \alpha = 0.05 $ At $ \alpha = 0.05 $, what is your conclusion? - Do not reject $ \mathrm{H_0} $. There is insufficient evidence to conclude that the percentage of supermarket shoppers who believe that supermarket ketchup is as good as the national brand ketchup is less than 62%. - Do not reject $ \mathrm{H_1} $. There is sufficient evidence to conclude that the percentage of supermarket shoppers who believe that supermarket ketchup is as good as the national brand ketchup

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