According to a Pew Research Center report from 2012, the average commute time to work in California is 27.5 minutes. To investigate whether a different average is true for the small city that she lives in, a California high school student surveys 45 people she knows—her teachers, her parents and their friends and co-workers—and finds the average commute time for this sample to be 24.33 minutes, with a standard deviation of 9.53 minutes.
a. Write out the null and alternative hypotheses for our test in words or in symbols.
b. Use the Theory-Based Inference applet to find and report a standardized statistic (t-statistic) and a p-value for the test.
c. Based on your p-value, write out a conclusion, being sure to include justification.
d. The data did not come from a random sample; rather it came from a convenience sample of people to whom the student had access. Given that information, to what population do you think we can generalize our results?