Lake Huron is one of the Great Lakes of North America. Its meandepth is recorded as being 577.5 feet. However, this is presumablya measurement of average depth over time, since the actual waterlevel varies from month to month. We are interested in testingwhether this reported mean depth of Lake Huron is plausible.

(a) State the appropriate null and alternative hypotheses.

Between 1875 and 1972, 98 depth measurements were taken for LakeHuron. The average depth from this sample of data was 579.0 feet,and the standard deviation of this sample was 1.32 feet.

(b) Calculate the appropriate standard error.

(c) Calculate the appropriate test-statistic.

(d) Use the tables in your course-book to find the p-value forthe test of your hypothesis. (e) Write a brief interpretation ofyour p-value, and what conclusion you would draw regarding yournull hypothesis.