Answered: Before changes to its management staff,…

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 14.2 minutes. The standard deviation of completion times was 1.5 minutes. An analyst at the company suspects that, under new management, the mean completion time, μ, is now less than 14.2 minutes. To test this claim, a random sample of 50 completion times under new management was taken by the analyst. The sample had a mean of 14.1 minutes. Can we support, at the 0.10 level of significance, the claim that the population mean completion time under new management is less than 14.2 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.)

Before changes to its management staff, an automobile assembly line operation had a scheduled mean completion time of 14.2 minutes. The standard deviation
of completion times was 1.5 minutes. An analyst at the company suspects that, under new management, the mean completion time, μ, is now less than 14.2
minutes. To test this claim, a random sample of 50 completion times under new management was taken by the analyst. The sample had a mean of 14.1
minutes. Can we support, at the 0.10 level of significance, the claim that the population mean completion time under new management is less than 14.2
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 Ho and the alternative hypothesis H₁.
H₂μ = 14.2
H, :μ < 14.2
(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 critical 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 14.2 minutes?
O Yes O No
μ
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X
#0
a
X
S
р
0=0 OSO ΠΣΠ
O<O
<e
00
□<ロ

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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