An umbrella salesperson has moved her base from Winnipeg to Atlantic Canada. Believing that the mean annual precipitation for communities in Atlantic Canada is over twice the annual amount in Winnipeg (526 mm), she expects to do a great business. Refer to the top eight entries for annual precipitation in Data Set 4 in Appendix B. Assuming these data are from a random selection of sites in Atlantic Canada, test the claim that the mean annual precipitation for communities in Atlantic provinces is greater than 1052 mm. Use the 0.05 level of significance.
Suppose the entries from Atlantic Canada in Data Set 4 were not selected randomly from all possible sites, but were selected based on population plus convenience of data collection. What would be the implications-theoretical and practical-for using the results of the t test?
Use the traditional approach summarized. Draw a graph showing the test statistic and critical values. In each case, assume that the population has a distribution that is approximately normal and that the sample is randomly selected.