Question

A sprinkler system for fire protection in buildings is required to have an average activation temperature of 130o F. A randomly selected sample of N = 12 systems are tested with an average sample activation temperature of x = 129.7o F. It is known that the distribution of activation temperatures is normally distributed with a standard deviation s = 1.25o F. using the P-value hypothesis test method, if the sample data contradicts the required average activation temperature at a significance level of a = 0.02?

Answer 1

Given that

sample mean (xbar) = 129.7, sample size n = 12, sample standard deviation s = 1.25 and population mean =130

test statistics t =

degree of freedom = n-1 = 12-1 = 11

using t statistics and df values with the t distribution table, we get

p value =0.4242

p value is greater than 0.02 significance level, we failed to reject the null hypothesis.

Therefore, we can say that there is insufficient evidence to conclude that the sample data contradicts the required average activation temperature at a significance level of a = 0.02