The Scottsdale fire department aims to respond to fire calls

The Scottsdale fire department aims to respond to fire calls in 6 minutes or less, on average. Response times are normally distributed with a standard deviation of 1.1 minute. Would a sample of 18 fire calls with a mean response time of 6 minutes 39 seconds provide sufficient evidence to show that the goal is not being met at ? = 0.01?

Calculate the value of Test statistic. (Carry out all intermediate calculations to at least four decimal places. Round your answer to 3 decimal places.)

Use Excel to find the p-value. (Round your answer to 4 decimal places.)

Solution

6 minutes 39 seconds = 6.65 minutes

The test statistic is

t=(xbar-mu)/(s/vn)

=(6.65-6)/(1.1/sqrt(18))

=2.507

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The degree of freedom =n-1=18-1=17

It is a right-tailed test.

So the p-value= P(t with df=17>2.507) =0.0113