### Hypothesis Testing Problems#### 1. **a.** A sample of \( n = 13 \) observations has a sample mean of \( \bar{x} = 2.879 \). If an assumed known standard deviation of \( \sigma = 0.325 \) is used, calculate the p-values for the hypothesis testing problems:- **(a)** \( H_0 : \mu = 3.0 \) versus \( H_A : \mu \neq 3.0 \).- **(b)** \( H_0 : \mu \geq 3.1 \) versus \( H_A : \mu < 3.1 \).**b.** 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 are 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)** Write down the null hypothesis and the alternative hypothesis that the experimenter should use for the test.- **(b)** For what values of the t-statistic does the experimenter accept the null hypothesis with a level of significance \( \alpha = 0.10 \)?- **(c)** Is the null hypothesis accepted or rejected with \( \alpha = 0.10 \)?- **(d)** Write down an expression for the p-value and estimate it.

Here AS PER POLICY I HAVE CALCULATED FIRST MAIN QUESTION . PLZ REPOST FOR QUESTION B

Answered: 1. A sample of n=13 observations has a…

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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1. A sample of n=13 observations has a sample mean of x= 2.879. If an assumed known standard deviation of o = 0.325 is used, calculate the p-values for the hypothesis testing problems: (a) Ho : µ = 3.0 versus HA :H 3.0. (b) Ho : µ>3.1 versus HA :µ < 3.1. а.