An Izod impact test was performed on 20 specimens of PVC pipe. The sample mean is...

An Izod impact test was performed on 20 specimens of PVC pipe. The sample mean is x Overscript bar EndScripts equals 1.44 and the sample standard deviation is s = 0.27. Find a 99% lower confidence bound on the true Izod impact strength. Assume the data are normally distributed. Round your answer to 3 decimal places. less-than-or-equal-to

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Expert Solution

Solution :

Given that,

Point estimate = sample mean = = 1.44

sample standard deviation = s = 0.27

sample size = n = 20

Degrees of freedom = df = n - 1 = 19

At 99% confidence level the t0.005 is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

t_/2,df = t_0.005,19 = 2.861

Margin of error = E = t_/2,df * (s / $\sqrt$ n)

= 2.861 * ( 0.27/ $\sqrt$ 20)

= 0.173

The 99% confidence interval estimate of the population mean is,

- E + E

1.44 - 0.173 1.44 + 0.173

1.267 1.613

(1.267 , 1.613)

orchestra answered 1 year ago

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