MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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![The breaking strengths of cables produced by a certain manufacturer have historically had a mean of 1800 pounds and a standard deviation of 75 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 1800 pounds. To see if this is the case, 42 newly manufactured cables are randomly chosen and tested, and their mean breaking strength is found to be 1832 pounds. Assume that the population is normally distributed. Can we support, at the 0.01 level of significance, the claim that the population mean breaking strength of the newly manufactured cables is greater than 1800 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 \( H_0 \) and the alternative hypothesis \( H_1 \).
\[ H_0: \square \]
\[ H_1: \square \]
(b) Determine the type of test statistic to use.
\[ \text{(Choose one)} \]
(c) Find the value of the test statistic. (Round to three or more decimal places.)
\[ \square \]
(d) Find the p-value. (Round to three or more decimal places.)
\[ \square \]
(e) Can we support the claim that the population mean breaking strength of the newly-manufactured cables is greater than 1800 pounds?
\[ \text{Yes} \]
\[ \text{No} \]
There is a diagram in the form of a calculator keypad with various symbols likely representing statistical notations for different tests, population parameters, etc.](https://content.bartleby.com/qna-images/question/b5da94fe-19e7-4c6f-a636-47d7a1fa1ee8/b957c8fb-e185-4554-ad10-19f655bd2a48/lq7lp9_processed.jpeg)
Transcribed Image Text:The breaking strengths of cables produced by a certain manufacturer have historically had a mean of 1800 pounds and a standard deviation of 75 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 1800 pounds. To see if this is the case, 42 newly manufactured cables are randomly chosen and tested, and their mean breaking strength is found to be 1832 pounds. Assume that the population is normally distributed. Can we support, at the 0.01 level of significance, the claim that the population mean breaking strength of the newly manufactured cables is greater than 1800 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 \( H_0 \) and the alternative hypothesis \( H_1 \).
\[ H_0: \square \]
\[ H_1: \square \]
(b) Determine the type of test statistic to use.
\[ \text{(Choose one)} \]
(c) Find the value of the test statistic. (Round to three or more decimal places.)
\[ \square \]
(d) Find the p-value. (Round to three or more decimal places.)
\[ \square \]
(e) Can we support the claim that the population mean breaking strength of the newly-manufactured cables is greater than 1800 pounds?
\[ \text{Yes} \]
\[ \text{No} \]
There is a diagram in the form of a calculator keypad with various symbols likely representing statistical notations for different tests, population parameters, etc.
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