The breaking strengths of cables produced by a certain manufacturer have historically had a mean of 1925 pounds and a standard deviation of 85 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 1925 pounds. To see if this is the case, 25 newly manufactured cables are randomly chosen and tested, and their mean breaking strength is found to be 1932 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 1925 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 H0 and the alternative hypothesis H1 . H0:μ=1925 H1:μ>1925 (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 breaking strength of the newly-manufactured cables is greater than 1925 pounds? 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

The breaking strengths of cables produced by a certain manufacturer have historically had a mean of

1925

pounds and a standard deviation of

pounds. The company believes that, due to an improvement in the manufacturing process, the mean breaking strength,

, of the cables is now greater than

1925

pounds. To see if this is the case,

newly manufactured cables are randomly chosen and tested, and their mean breaking strength is found to be

1932

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

1925

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 H0 and the alternative hypothesis H1 .
H0:μ=1925
H1:μ>1925
(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 breaking strength of the newly-manufactured cables is greater than 1925 pounds?
Yes No

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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