Question 1169557: The registrar's office at State University would like to determine a 95% confidence interval for the mean commute time of its students. A member of the staff randomly chooses a parking lot and surveys the first 200 students who park in the chosen lot on a given day. The confidence interval is
meaningful because the sample is representative of the population.
not meaningful because of the lack of random sampling.
not meaningful because the sampling distribution of the sample mean is not normal.
meaningful because the sample size exceeds 30 and the Central Limit Theorem ensures normality of the sampling distribution of the sample mean.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! It is not meaningful because of the lack of random sampling.
The problem is the first 200 students who park in the lot are not necessarily representative of the mean commute time. Those who come later may have different traffic patterns, may have been delayed, and the commute time may be quite different if one leaves a few minutes earlier or later. The plan would give an idea of the commute time, perhaps to then design a randomized study to look at it in more detail.
The sample may well be normally distributed, and if not, the size of the sample may well allow one to treat it as normal, assuming no skew.
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