Answered: The breaking strengths of cables…

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 breaking strengths of cables produced by a certain manufacturer have historically had a mean of 1750 pounds and a standard deviation of 95 pounds. The company believes that, due to an improvement in the manufacturing process, the mean breaking strength, μ, of the cables is now greater than 1750 pounds. To see if this is the case, 11 newly manufactured cables are randomly chosen and tested, and their mean breaking strength is found to be 1815 pounds. Assume that the population is normally distributed. Can we support, at the 0.05 level of significance, the claim that the population mean breaking strength of the newly-manufactured cables is greater than 1750 pounds? Assume that the population standard deviation 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.)

The breaking strengths of cables produced by a certain manufacturer have historically had a mean of 1750 pounds and a
standard deviation of 95 pounds. The company believes that, due to an improvement in the manufacturing process, the
mean breaking strength, μ, of the cables is now greater than 1750 pounds. To see if this is the case, 11 newly
manufactured cables are randomly chosen and tested, and their mean breaking strength is found to be 1815 pounds.
Assume that the population is normally distributed. Can we support, at the 0.05 level of significance, the claim that the
population mean breaking strength of the newly-manufactured cables is greater than 1750 pounds? Assume that the
population standard deviation 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 Ho and the alternative hypothesis H₁.
Ho :O
H₁ :0
(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.)
0
(d) Find the p-value. (Round to three or more decimal places.)
0
(e) Can we support the claim that the population mean breaking strength of the
newly-manufactured cables is greater than 1750 pounds?
O Yes O No
3
XI
0=0
a
X
S
90
OSO
#0 ロ<ロ
Р
<Q
Ś
00
ロマロ
O>O

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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