Question

Clearly label your responses (Question 1.a, Question 1.b., etc.), show all your work, results, figures and interpretation in the Word document. At the end of the Word document, create a section entitled “Appendix: R Syntax”, and copy and paste all the R codes you used for each question part.

A 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 4.5 minutes provide sufficient evidence to show that the goal is not being met at the significance level α = .01? Is this a left-tailed, right-tailed, or two-tailed test? Formulate null and alternative hypothesis. Compute the appropriate test statistic and critical value using R. What is the statistical decision? Interpret the results.

Answer 1

The R code is:

mu = 4
s = 1
xbar = 4.5
n = 18
se <- s/sqrt(n)
z = (xbar - mu)/se
pnorm(z, lower.tail = FALSE)

The hypothesis being tested is:

H₀: µ $\leq$ 4

H_a: µ > 4

The test statistic, z = 2.12

The p-value is 0.01694743.

Since the p-value (0.01694743) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we can conclude that the fire department aims to respond to fire calls in 4 minutes or less, on average.