The scottsdale fire department aims to respond to fire calls in 4 minutes or less, on average. response times are normally distributed with a standard deviation of 1 minute. would a sample of 18 fire calls with a mean response time of 4 minutes 30 seconds provide sufficient evidence to show that the goal is not being met at α = .01?

Let be the population mean.

As per given , we have

Since the alternative hypothesis is right-tailed , so the test is a right-tailed test.

Also, population standard deviation is given , so we perform one-tailed z-test.

Test statistic :

, where = Population mean

= Population standard deviation

n= sample size

= Sample mean

For n= 18 , , , , we have

P-value (for right tailed test): P(z>2.12) = 1-P(z≤ 2.12)  [∵ P(Z>z)=1-P(Z≤z)]\

=1- 0.0340=0.9660

Decision : Since P-value(0.9660) > Significance level (0.01), it means we are failed to reject the null hypothesis.

[We reject null hypothesis if p-value is larger than the significance level . ]

Conclusion : We do not have sufficient evidence to show that the goal is not being met at α = .01 .

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