**Hypothesis Testing Example**12. A food manufacturer claims that at the time of purchase by a consumer, the average age of its product is no more than 120 days. In an experiment to test this claim, a random sample of 36 items is found to have ages at the time of purchase with a sample mean of $ \bar{x} = 122.5 $ days and a sample standard deviation of $ s = 13.4 $ days.(a) **Null Hypothesis ($ H_0 $) and Alternative Hypothesis ($ H_a $):** - Null Hypothesis ($ H_0 $): The average age of the product at the time of purchase is 120 days or less. ($ \mu \leq 120 $) - Alternative Hypothesis ($ H_a $): The average age of the product at the time of purchase is greater than 120 days. ($ \mu > 120 $)(b) **Values of the t-statistic at a significance level ($ \alpha = 0.10 $):** - To accept the null hypothesis, we calculate the t-statistic and compare it to the critical t-value from the t-distribution with $ n-1 = 35 $ degrees of freedom.(c) **Hypothesis Test Decision at $ \alpha = 0.10 $:** - Using the calculated t-statistic and comparing it against the critical value, decide whether to accept or reject the null hypothesis at the 10% significance level.(d) **Expression for the p-value and Estimate:** - Calculate the p-value using the t-statistic. The p-value indicates the probability of observing a result as extreme as the sample mean under the null hypothesis. - Estimate the p-value using statistical software or a t-distribution table.**Note:** Detailed calculations and the critical value lookup would typically be performed using statistical resources or software.

We have given that Sample size n= 36 , xbar= 122.5 s= 13.4 and mu= 120 level of significance =alpha…

Answered: 12. A food manufacturer claims that at…

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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iii
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