Problem 5 A valve manufacturer produces a butterfly valve composed of two semici

Question

Problem 5 A valve manufacturer produces a butterfly valve composed of two semicircular plates on a common spindle that is used to permit flow in one direction only (seen here: http://en.wikipedia.org/wiki/Butterfly_valve). The manufacturer produces valves in five different factories: Pawhuska, Barnsdát, Wynona, Fairfax, and Shidler. The precision of the valve, measured as the magnitude of deviation from the specification in 1/100 inch, is provided in the Problem 5 spreadsheet tab for a random sample of valves produced at each factory. Is there a difference in the valves being produced at the facilities, as measured by precision? If so, use the Tukey test to further analyze the factories, highlighting the best performing and worst performing factories. Use R.

Explanation / Answer

95% Confidence Interval => alpha = 0.05

SInce Population standard deviation is not mentioned, t scores are calculated

95% Confidence Interval for mean

( xbar - t(alpha/2,n-1)*std.dev/sqrt(n) , xbar + t(alpha/2,n-1)*std.dev/sqrt(n) )

Here, x bar = Sample mean of 20 observations = 2.36237

t(alpha/2, n-1) = t(.025,19) = 2.093

standard deviation = 0.19555

Therefore, 95% onfidence Interval becomes

= (2.36237 - 2.093*0.19555/sqrt(20), 2.36237 + 2.093*0.19555/sqrt(20)))

= (2.27085,2.45389)

Point estimate = sample mean = 2.36237

Error of the interval = Critical value x Standard error of the statistic

= 2.093*0.19555/sqrt(20)

= 0.09152

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