### Hypothesis Testing on Light Bulb LifetimesA manufacturer claims that the mean lifetime, $ \mu $, of its light bulbs is 44 months. The standard deviation of these lifetimes is 7 months. Twenty-four bulbs are selected at random, and their mean lifetime is found to be 45 months. Assume that the population is normally distributed. We want to determine if, at the 0.01 level of significance, the mean lifetime of light bulbs made by this manufacturer differs from 44 months.**Perform a Two-Tailed Test:**Complete the following steps:1. **State the Hypotheses:** - **Null Hypothesis ($H_0$):** $ \mu = 44 $ - **Alternative Hypothesis ($H_1$):** $ \mu \neq 44 $2. **Determine the Type of Test Statistic to Use:** - Choose a test statistic based on the data provided and the nature of the hypothesis.3. **Find the Value of the Test Statistic:** - Calculate this value and round it to three or more decimal places.4. **Find the p-value:** - Compute the p-value for the test statistic, rounding to three or more decimal places.5. **Conclusion:** - Decide if the mean lifetime of light bulbs differs from 44 months based on the p-value. - Select either "Yes" or "No" to indicate if there is a significant difference.**Icons Explanation:**Icons shown in the image are indicative of common statistical symbols and operations, such as the normal distribution and various arithmetic calculations.Please refer to a list of statistical formulas if necessary, and be sure to carry your intermediate computations to three or more decimal places for accuracy.

Answered: A manufacturer claims that the mean…

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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