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 70 bulbs at random. For the bulbs in the sample, the mean lifetime is 56 months. It is known that the population standard deviation of the lifetimes is 7 months. Can we conclude, at the 0.10 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. Then complete the parts below.Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.)(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.[Choose one] [ ](c) Find the value of the test statistic. (Round to three or more decimal places.)[ ](d) Find the two critical values. (Round to three or more decimal places.)[ ] and [ ](e) Can we conclude that the population mean lifetime of light bulbs made by this manufacturer differs from 54 months?Yes [ ] No [ ]---**Explanation of Graph/Diagram:**The image contains a section for statistical hypothesis testing with fields for inputting calculations. No graphs or diagrams are included in this section. **Title:** Hypothesis Testing for a Marriage Counselor's Program EffectivenessA marriage counselor has traditionally observed that the proportion \( p \) of all married couples for whom the communication program can prevent divorce is 77%. After making recent changes, the counselor now claims that the program can prevent divorce in more than 77% of married couples. In a random sample of 230 married couples who completed the program, 190 stayed together. Is there enough evidence to support the marriage counselor's claim at the 0.01 level of significance?**Steps for Hypothesis Testing:**1. **State the Hypotheses:** - **Null Hypothesis \( H_0 \):** \( p = 0.77 \) - **Alternative Hypothesis \( H_1 \):** \( p > 0.77 \)2. **Determine the Type of Test Statistic to Use:** Choose the appropriate statistical test for hypothesis testing from the available options.3. **Calculate the Test Statistic:** Perform the calculation and round to three or more decimal places.4. **Find the \( p \)-Value:** Calculate the \( p \)-value from the test statistic and round to three or more decimal places.5. **Conclusion:** Determine if there is enough evidence to support the marriage counselor's claim that the proportion of married couples who can prevent divorce is more than 77%. - **Decision:** - Yes \(\square\) - No \(\square\)**Note:** Always carry your intermediate computations to three or more decimal places to ensure accuracy. If necessary, consult a list of statistical formulas to complete the calculations.

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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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