Question

In: Statistics and Probability

Problem 2 A study was conducted to see how long Dr. Kennedy’s patients had to wait...

Problem 2
A study was conducted to see how long Dr. Kennedy’s patients had to wait before their appointment. A random sample of 30 patients showed the average waiting time was 20 minutes with a standard deviation of 16 minutes.


(a) Construct a 99% confidence interval for µ, the true mean waiting time and interpret your results.


(b) Suppose that Dr. Kennedy worker claims that the average waiting time at his hospital is 20 minutes. Based on the interval above, can this claim be rejected?

Solutions

Expert Solution

We need to construct the confidence interval for the population mean . Populaton standerd deviation is given hence One sample Z test is most appropriate here.
Confidence interval for Z test is given by:
  
where,  
Sample Mean
Population Standard Deviation =
Sample size (n)=30

The critical value of Z at is

Therefore substituting the values we get C.I as:
​

b) Therefore, based on the data provided, the confidence interval for the population mean is which indicates that we are confident that the true population mean is contained by the interval (12.476, 27.524).
And the value 20 lies in this interval. Hence Dr. Kennedy worker's claims that the average waiting time at his hospital is 20 minutes can NOT be rejected

orchestra answered 1 year ago
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