Question 1
In order to determine whether or not a drivers education course improves the scores on a driving exam, a sample of 6 students were given the exam before and after taking the course. The results are shown below.
Let d = Score After - Score Before.
|
Student
|
Score Before the Course
|
Score After the Course
|
|
1
|
83
|
87
|
|
2
|
89
|
88
|
|
3
|
93
|
91
|
|
4
|
77
|
77
|
|
5
|
86
|
93
|
|
6
|
79
|
83
|
We want to determine if the driver's education COurSe was effective.
a. Give the hypotheses for this problem.
b. Compute the test statistic.
c. At 95% confidence, test the hypotheses. That is, test to see if taking the course actually increased scores on the driving exam.
Question 2
In order to determine whether or not the number of automobiles sold per day (y) is related to price (x1 in $1,000), and the number of advertising spots (x2), data were gathered for 7 days. Part of the Excel output is shown below:
|
ANOVA
|
|
|
|
|
|
|
df
|
SS
|
MS
|
F
|
|
Regression
|
|
40.700
|
|
|
|
Residual
|
|
1.016
|
|
|
|
Coefficients Standard Error
|
|
Intercept
|
0.8051
|
|
|
|
|
X1
|
0.4977
|
0.4617
|
|
|
|
X2
|
0.4733
|
0.0387
|
|
|
a. Determine the least squares regression function relating y to x1 and x2.
b. If the company charges $20,000 for each car and uses 10 advertising spots, how many cars would you expect them to sell in a day?
c. At alpha = 0.05, test to determine if the fitted equation developed in Part a represents a significant relationship between the independent variables and the dependent variable.
d. At alpha = 0.05, test to see if the coefficient of x1 is significantly different from zero.
e. Determine the multiple coefficient of determination.