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Probability and Statistics for Eng...

9th Edition
Jay L. Devore
ISBN: 9781305251809

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BuyFindarrow_forward

Probability and Statistics for Eng...

9th Edition
Jay L. Devore
ISBN: 9781305251809
Textbook Problem

Exercise 1.13 gave a sample of ultimate tensile strength observations (ksi). Use the accompanying descriptive statistics output from Minitab to calculate a 99% lower confidence bound for true average ultimate tensile strength, and interpret the result.

images

N Mean Median TrMean StDev SE Mean
153 135.39 135.40 135.41 4.59 0.37
Minimum Maximum Q1 Q3
122.20 147.70 132.95 138.25

To determine

Find the 99% lower confidence bound for the population mean ultimate tensile strength.

Explanation

Given info:

The data represents the summary statistics for a sample of ultimate tensile strength.

Calculation:

Critical value:

For 99% level of confidence,

1α=10.99α=0.01

From Table A.3 of the standard normal distribution in Appendix , the critical value is 2.33.

Thus, the critical value is (zα)=2.33.

Point estimate:

Point estimate is the single value obtained from point estimation on a set of sample data as a parameter for the population.

The point estimate of the population mean μ is the sample mean (x¯) and it is an unbiased estimator of population mean.

From the MINITAB, the sample mean ultimate tensile strength is x¯=135.39ksi and the standard deviation is s=4

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