Problem 2. Face masks worn by firemen should withstand high temperatures. Fireme

Question

Problem 2. Face masks worn by firemen should withstand high temperatures. Firemen commonly work in temperatures of 200 - 500° F. In a test of one type of mask, 12 of 50 Tnasks had lenses pop out at 230°. Construct a 85% upper confidence bound for the true proportion of masks of this type whose lenses would pop out at 230° (a) Compute the bound using a variation of the result shown in the Class Notes, page 438, Proposition 25.2 (b) Compute the bound using the R command binom.test(). See in the class Notes, the computations shown at the top of page 439. Caution: use the correct alternative and confidence level.

Explanation / Answer

a)

Standard error of the mean = SEM = x(N-x)/N3 = 0.060

= (1-CL)/2 = 0.075

Standard normal deviate for = Z = 1.440

Proportion of positive results = P = x/N = 0.240

Lower bound = P - (Z*SEM) = 0.153

Upper bound = P + (Z*SEM) = 0.327

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