Before changes to its management staff, an automobile assembly line operation had a scheduled mean completion time of 13.2 minutes. The standard deviation of completion times was 1.7 minutes. An analyst at the company suspects that, under new management, the mean completion time, μ , is now less than 13.2 minutes. To test this claim, a random sample of 15 completion times under new management was taken by the analyst. The sample had a mean of 12.8 minutes. Assume that the population is normally distributed. Can we support, at the 0.01 level of significance, the claim that the population mean completion time under new management is less than 13.2 minutes? Assume that the population standard deviation of completion times has not changed under new management. 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 H0 and the alternative hypothesis H1 . H0:μ=13.2 H1:μ<13.2 (b) Determine the type of test statistic to use. ▼Z (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 population mean completion time under new management is less than 13.2 minutes? Yes No

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

Before changes to its management staff, an automobile assembly line operation had a scheduled mean completion time of

13.2

minutes. The standard deviation of completion times was

1.7

minutes. An analyst at the company suspects that, under new management, the mean completion time,

, is now less than

13.2

minutes. To test this claim, a random sample of

completion times under new management was taken by the analyst. The sample had a mean of

12.8

minutes. Assume that the population is normally distributed. Can we support, at the

0.01

level of significance, the claim that the population mean completion time under new management is less than

13.2

minutes? Assume that the population standard deviation of completion times has not changed under new management.

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 H0 and the alternative hypothesis H1 .
H0:μ=13.2
H1:μ<13.2
(b)	Determine the type of test statistic to use.
	▼Z
(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 population mean completion time under new management is less than 13.2 minutes?
Yes No

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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