A columnist for the LA Times is working to meet a deadline on a story about commuting in Los Angeles. She wants to include information about the current price of gasoline in the Los Angeles metro area, but her source person for this type of information has already gone home for the day. So, she decides to take her own sample as she drives home, writing down the prices she observes as she makes her way from downtown to her neighborhood in the suburbs. Below is the data sample she obtains (units are $/gallon).

Question

(A) Do you think she has obtained a true random sample?
?
(B) What average price could she report, based on the above sample?
 
(C) What is the 95% confidence interval for the average price range, based on the above sample?
 

(D) Do you see any issues with the 95% confidence interval calculated in part (C)?

What will be an ideal response?

Answer 1

?(A) For a true random sample, all possible gas stations in the LA metro area must have an equal chance of being sampled. In this case, only the stations on her route home were sampled, although they do at least represent a variety of settings (different parts of town). Given her time constraints, this sample may suffice, though.?(B) The sample mean is $3.23.?(C) Using the sample mean and sample standard deviation (0.185), the 95% confidence interval for the true mean price is approximately $3.15/gallon to $3.30/gallon.?(D) The sample, in addition to perhaps not being truly random, may also be too small to justify using the assumptions used calculating the range in (C). Typically we want n>30 unless the population data is approximately normal as well.?