Answered: The quality-control manager at 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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Question

The quality-control manager at a compact fluorescent light bulb (CFL) factory needs to determine whether the mean life of a large shipment of CFLs is equal to 7520 hours. The population standard deviation is 910 hours . A random sample of 49 light bulbs indicates a sample mean life of 7312 hours. a. At the 0.05 level of significance, is there evidence that the mean life is different from 7520 hours ? b. Compute the p-value and interpret its meaning. c. Construct a 95% confidence interval estimate of the population mean life of the light bulbs. d. Compare the results of (a) and (c). What conclusions do you reach? e. Compare the results of parts (a) through (d) to those when the standard deviation is hours. Question content area bottom Part 1 a. Let µ be the population mean. Determine the null hypothesis, H0, and the alternative hypothesis,H1 . H0 : µ ▼ equals not equals less than or equals greater than or equals enter your response here H1 : µ ▼ less than equals greater than not equals enter your response here

Part 2 What is the test statistic?

Z stat = enter your response here (Round to two decimal places as needed.)

Part 3 What is/are the critical value(s)?

-----enter your response here (Round to two decimal places as needed. Use a comma to separate answers as needed.)

Part 4 What is the final conclusion?

A. Reject H0. There is sufficient evidence to indicate that the mean life is different from 7520 hours.

B. Fail to reject H0 . There is sufficient evidence to indicate that the mean life is different from 7520 hours.

C. Fail to reject H0. There is sufficient evidence to indicate that the mean life is different from 7520 hours.

D. Reject H0. There is sufficient evidence to indicate that the mean life is different from 7520 hours.

b. What is the p-value? enter your response here (Round to three decimal places as needed.)

Part 6 Interpret the meaning of the p-value. The p-value is the probability of obtaining a ▼ sample population with a mean ▼ equal to at least as extreme as less extreme than enter your response here hours, given that the ▼ alternative null hypothesis is true.

Part 7 c. Construct a 95% confidence interval estimate of the population mean life of the light bulbs. ___≤µ≤____ enter your response here enter your response here (Round to the nearest whole number as needed.)

Part 8 d. Compare the results of (a) and (c). What conclusions do you reach?

A. The results of (a) and (c) are not the same. There is sufficient evidence to indicate that the mean life is different from 7520 hours.

B. The results of (a) and (c) are not the same. There is sufficient evidence to indicate that the mean life is different from 7520 hours.

C. The results of (a) and (c) are the same. There is sufficient evidence to indicate that the mean life is different from 7520 hours.

D. The results of (a) and (c) are the same. There is sufficient evidence to indicate that the mean life is different from 7520 hours.

Part 9 e. Compare the results of parts (a) through (d) to those when the standard deviation is 700. When the standard deviation is , 700, Zstat = -2.08 the p-value is 0.038, and the 95% confidence interval is 7,116 ≤µ≤7,508. State the conclusion for the new standard deviation using the critical value approach. Compare the results to part (a).

Using the critical value approach, H0. ▼ do not reject reject . This result is ▼ different from the same as the result found in part (a) because Zstat has ▼ decreased not changed increased in absolute value.

Part 10 State the conclusion for the new standard deviation using the p-value approach. Compare the results to part (b).

Using the p-value approach, ▼ reject do not reject H0 . This result is ▼ the same as different from the result found in part (b) because the p-value has ▼ not changed. increased. decreased.

Part 11 State the conclusion for the new standard deviation using the confidence interval approach. Compare the results to part (c).

Using the confidence interval approach, ▼ reject do not reject H0 . This result is ▼ different from the same as the result found in part (c), because the confidence interval has ▼ not changed. become narrower. become wider.

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