1. The data below are monthly average daily temperatures (F) for two sites around St. Louis, MO for 5 years. Use these two samples to see if there is a statistically significant difference between the samples and the 30-yr airport data (the population). If there is a difference, we may continue our studies to see if there is an Urban Heat Island effect. (NOTE: The observations were taken at the same time each day for both locations. Instruments were calibrated similarly prior to data collection. All data are rounded to the nearest integer).

Month Downtown Rural

Jan 36 33

Feb 40 35

Mar 48 44

April 63 59

May 75 70

June 82 77

July 85 81

Aug 84 79

Sep 78 74

Oct 69 62

Nov 54 47

Dec 41 36

The two samples are: "Downtown" and "Rural". Using these data, calculate two separate one-sample t-tests (one for each sample) to see how the 'Downtown' and 'Rural' samples compare to the population mean at Lambert International Airport, which is 61.38F.

Part 1. Calculate the sample means for downtown and rural.

Here are the standard deviations for the calculations:

Downtown SD= 18.44

Rural SD=18.34

NOTE: we are testing to see whether or not there is a statistica y significant difference in the means. We are NOT specifying the direction (> or <) of that difference. Test using significance levels of: 0.01 and 0.05.

NOTE: take the absolute value of your calculated t-value when comparing it to your t-critical value. A negative t-value only means that the sample mean was less than the population mean. For example: if you calculate a t-value of -2.91, use the absolute value (2.91) as the value to compare to the t-critical value (see the small print at the bottom of p.98 in your text for more info).

1a) Construct null and alternate/research hypotheses for each test.

1b] What is your t-critical value? [at the 1% and 5% significance levels]

1c] What are your calculated t-values for each test? Downtown = R u r a l =

1d] What did you conclude in each test? Did you reject or fail to reject your nu hypothesis [in each case]? Downtown = R u r a l =

1e] What does the results mean?