A leakage test was conducted to determine the effectiveness of a seal designed t

Question

A leakage test was conducted to determine the effectiveness of a seal designed to keep the inside of a plug airtight. An air needle was inserted into the plug, and the plug and needle were placed under water. The pressure was then increased until leakage was observed. Let X equal the pressure in pounds per square inch. Assume that the distribution of X is N(mu, sigma^2). The following n = 10 observations of X were obtained: 3.1 3.3 4.5 2.8 3.5 3.5 3.7 4.2 3.9 3.3 Use the observations to (a) Find a point estimate of mu. (b) Find a point estimate of sigma. (c) Find a 95% one-sided confidence interval for mu that provides an upper bound for mu.

Explanation / Answer

a)
point estimate of mean = sum of all numbers / total number
= 3.58

b) Point estimate of std.deviation = summation of ( x - mean)^2 / (n - 1) = 0.5116

c)
z value at 95% CI = 1.96

CI = mean + /- z *(s/sqrt(n))
= 3.58 + /- 1.96 * ( 0.5116 / sqrt(10))
= (3.263 , 3.897)
Upper bound = 3.897

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