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 agoRelated Solutions
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