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Statistical Analysis - Testing hypotheses by the five-step procedure

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The breaking strengths of cables produced by a certain manufacturer have a mean of 1750 pounds, and a standard deviation of 60 pounds. It is claimed that an improvement in the manufacturing process has increased the mean breaking strength. To evaluate this claim, 80 newly manufactured cables are randomly chosen and tested, and their mean breaking strength is found to be 1752 pounds. Can we support, at the .05 level of significance, the claim that the mean breaking strength has increased? (Assume that the standard deviation has not changed.)
Perform a one-tailed test.
1. Null hypothsis
2 Hypothesis
3. Type of statistic z t chi f
4. Value of test statistic
5. The p-value
6. Can we support that the mean breaking strength has increased.

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The solution contains detailed explanation of testing hypotheses using the five-step procedures.

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The breaking strengths of cables produced by a certain manufacturer have a mean, , of 1750 pounds, and a standard deviation of 60 pounds. It is claimed that an improvement in the manufacturing process has increased the mean breaking strength. To evaluate this claim, 80 newly manufactured cables are randomly chosen ...

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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