**Statistical Hypothesis Testing of Light Bulb Lifetimes**According to a report done by S & J Power, the mean lifetime of the light bulbs it manufactures is 54 months. A researcher for a consumer advocate group tests this by selecting 44 bulbs at random. For the bulbs in the sample, the mean lifetime is 50 months. It is known that the population standard deviation of the lifetimes is 9 months. Assume that the population is normally distributed. Can we conclude, at the 0.01 level of significance, that the population mean lifetime, μ, of light bulbs made by this manufacturer differs from 54 months?**Perform a Two-tailed Test**To conduct this analysis, follow the steps below:(a) **State the Null Hypothesis $ H_0 $ and the Alternative Hypothesis $ H_1 $:**- $ H_0: $ - $ H_1: $ (b) **Determine the Type of Test Statistic to Use:**- Select the appropriate test statistic from the options.(c) **Find the Value of the Test Statistic:**- Perform the calculations and round the result to three or more decimal places.(d) **Find the Two Critical Values:**- Determine the critical values for this analysis, rounding to three or more decimal places.(e) **Conclusion:**- Decide whether the population mean lifetime of light bulbs made by this manufacturer differs from 54 months. - $ \text{Yes} $ - $ \text{No} $**Note:** Ensure all intermediate computations are carried out to three or more decimal places, and refer to any necessary formulas as needed.**Guidance on Symbols and Notations:**- Use the provided symbols and structures to fill in the hypothesis statements and calculation values. These include symbols for mean (μ), standard deviation (σ), population mean (p), sample mean ($ \bar{x} $), and standard score (z).

GivenMean(x)=50standard deviation(σ)=9sample size(n)=44α=0.01

Answered: According to a report done by S & J…

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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