Prestressing wire for wrapping concrete pipe is manufactured in large rolls and

Question

Prestressing wire for wrapping concrete pipe is manufactured in large rolls and is normally distributed. A quality control inspector required 45 samples from a roll to be tested for ultimate tensile strength (in 1000psi). x^- = 256.6, sigma = 2.73. a. Create a 95% confidence interval for the population mean tensile strength. b. The manufacturer claims that the population mean tensile strength is greater than 255. Does the confidence interval verify this claim? c. What is the lowest sample size that could be used to give reliable results on the confidence interval if the confidence level was 99%?

Explanation / Answer

Mean = 256.6,

SD = 2.73

a) The 95% confidence interval will be mean +/- 1.96 s

s = SD / sqrt(n)

Thus, the required interval will be:

256.6 +/- 1.96 * 2.73/sqrt(45)

= 256.6 +/- 0.7976

= ( 255.8, 257.4)

since 95% of the pipes tested would lie in the range of 255.80 to 257.39 psi both of which are above 255, the claim of the manufacturer can be supported.

The margin of error in this case should be equal to it's least count = 0.1

Thus, sample size for 99% accuracy will be:

0.79765 = 2.58 * 2.73 / sqrt(n)

n = 77.72

Thus, 78 people will be required for the same at 99% confidence

Hop this helps.

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