**Title: Hypothesis Testing for Automobile Assembly Line Completion Time**An automobile assembly line operation has a scheduled mean completion time, \( \mu \), of 15.1 minutes. The standard deviation of completion times is 1.2 minutes. It is claimed that, under new management, the mean completion time has decreased. To test this claim, a random sample of 70 completion times under new management was taken. The sample had a mean of 14.9 minutes. Can we support, at the 0.05 level of significance, the claim that the mean completion time has decreased under new management? Assume that the standard deviation of completion times has not changed.Perform a **one-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 \( p \)-value.** (Round to three or more decimal places.)[ ]**(e) Can we support the claim that the mean completion time has decreased under new management?**[ ] Yes [ ] No---**Explanation of Elements:**- **Null Hypothesis (\( H_0 \)):** The statement that the mean completion time has not decreased from the original mean of 15.1 minutes.- **Alternative Hypothesis (\( H_1 \)):** The statement that the mean completion time has decreased from the original mean of 15.1 minutes.- **Test Statistic Selection:** Choose the appropriate test statistic based on the given dataset and assumptions.- **Test Statistic Calculation:** Compute the statistic that will be compared against a critical value or used to find the \( p \)-value.- **\( p \)-value Calculation:** Determine the probability of observing the sample data (or something more extreme) assuming that the null hypothesis is true.- **Conclusion:** Decide whether there is enough evidence to support the claim that the mean completion time has decreased.

Given,sample size(n)=70sample mean(x¯)=14.9standard deviation(σ)=1.2α=0.05

Answered: An automobile assembly line operation…

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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