Question

An industrial engineer concerned with service at a large medical clinic recorded the duration of time from the time a patient called until a doctor or nurse returned the call. A sample of size 180 calls had a mean of 1.65 hours and a standard deviation of 0.82.

a) Obtain a 95% confidence interval for the population mean of time to return a call.

b) Does μ lie in your interval obtained in part (a)? Explain.

c) Perform a test (using critical value approach) with the intention of establishing that the mean time to return a call is greater than 1.5 hours. Use α = 0.05. Also confirm your decision using p-value approach.

d) In light of your conclusion in part (a), what error could you have made? Explain in the context of this problem.

e) In a long series of repeated experiments, with new random samples collected for each experiment, what proportion of the resulting tests would reject the null hypothesis if it prevailed? Explain your reasoning

Answer 1

Given the sample size n = 180 and sample mean = 1.65, sample standard deviation s = 0.82
The (1 - alpha) 100% two sided confidence interval for population mean based on the sample data is
a) The 95% CI is
b) If population mean is mu = 1.5, it does not lie in the above interval.
c)The hypotheses are
The test statistic is
The critical value for this right tailed test is Z1-a = 1.644854
Since the test statistic is greater than critical value is
Reject the null hypothesis. That is the mean time to return a call is greater than 1.5 hours