1. ( 60 pts) The results of a sample of 7 data points are presented below in terms of the Average Daily Temperature (^oF) and the Average Monthly Precipitation (inches):

Average Daily temperature x	86	81	83	89	80	74	64
Average Monthly Precipitation y	3.4	1.8	3.5	3.6	3.7	1.5	0.2

1. (10 pts) Draw a scatter plot

1. (5 pts) Compute the correlation coefficient
2. (10 pts) State the hypothesis and test the correlation significance at a = 0.01
3. (5 pts) Determine the regression line equation
4. (10 pts) Plot the regression line on the scatter plot (on same graph)
5. (10 pts) Calculate the standard error of estimate
6. (10 pts) Find the 95% prediction interval for the 95^oF average daily temperature

1. (20 pts) A researcher claims that the standard deviation of the ages of cats is greater than the standard deviation of dogs who are owned by families in a large city. A randomly selected sample of 29 cats has a standard deviation of 3.5 years, and a random sample of 16 dogs has a standard deviation of 2.7 years. Is the researcher correct at a = 0.05.

1. (20 pts) A composition teacher wishes to see whether a new grammar program will reduce the number of grammatical errors her students make when writing a two page essay. The data are shown here. At a = 0.025, can it be concluded that the numbers of errors has been reduced?

Student	1	2	3	4	5	6
Errors Before	12	9	0	5	4	3
Errors After	9	6	1	3	2	3