From sampled data, state the distribution used to calculate the confidence interval on the mean. Also, state the distribution that is used to calculate the confidence interval on the standard deviation.
The following data give the difference between actual arrival time and scheduled arrival time for the 12 monthly flights someone made into his/ her resident city during the previous year (plus values indicate the number of minutes the flight was late). The traveler was always scheduled to arrive at the same time on the last Wednesday of the month.
(a) Determine the sample mean and standard deviation.
(b) Estimate the 95% confidence intervals for the population mean and standard deviation. Note any assumptions.
(c) Display data in a histogram format.
(d) Create a normal probability plot of the data.
(e) Estimate arrival time range for 90% of the flights (using normal probability plot and Z table (Table A). Comment on analysis.
(f ) Interpret the plots and describe any further investigation.
(g) If someone was to make a general inference about the arrival times of all passengers into the airport, state a key underlying assumption that is violated.
(h) Explain the potential problem with making inferences about next year’s arrival times from the current year’s arrival times.