Q1: Gas Station
An owner of a gas station in Ottawa would like to estimate the mean number of litres (L) of gasoline sold to his customers based on a random sample of 10 sales. Historically, the number of litres (L) of gasoline sold follows a Normal distribution with a mean of 50L and a standard deviation of 8L. In practice, these numbers are unknown to the owner of the gas station.
(a) Use the SPSS procedure demonstrated in Lab 5 to generate 100 independent random samples of size n=10 from the gasoline sales, and to compute the corresponding 100 confidence intervals for the population mean gasoline using a 95% confidence level. When computing the confidence intervals, assume the population standard deviation is not known.
(b) Prior to generating your 100 samples, how many of your confidence intervals did you expect to capture the population mean? According to your output in part (a), how many of the 100 confidence intervals successfully captured the population mean? Why will these two values not necessarily be the same?
(c) State the mean and standard deviation from your first sample, and use these to re-compute the 95% confidence interval for the population average gasoline sold without using SPSS. Interpret the result.
Q2: CTV News
CTV News is Canada's most-watched news organization both locally and nationally.
(a) Assume that you do not have any prior knowledge of the proportion of CTV News watchers at Carleton University. Determine the sample size required in order to be 99% confident that the sample proportion of CTV News watchers at Carleton University is within a margin of error of 1% of the population proportion.
(b) Suppose that in a random sample of 100 students from Carleton University in January 2024, 72 students indicated they watch CTV News every day. Calculate and interpret a 95% confidence interval for the proportion of CTV News watchers among Carleton University students.
(c) What conditions and assumptions are required for the confidence interval to be valid?