Question

** Please only use RStudio to solve this problem and show code **

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.

** Please only use RStudio to solve this problem and show code **

Answer 1

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R-Code

> mu = 4 #Population mean
> n = 18 #sample Size
> xbar = 4.5 #sample mean
> s = 1 #standard dev
> z = (xbar - mu)*sqrt(n)/s # Test statistics
> z
[1] 2.12132
> CV = qnorm(0.99)
> CV
[1] 2.326348

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Since, test statistics is less than the critical value. So, Fail to reject the null hypothesis

There is no sufficient evidence to show that the goal is not being met at the significance level