At alpha 005 test to see if the coefficient of x1 is

Question

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.

Answer 1

Simplify the following statistics problem by considering the case situation and provide answer by showing the complete process of solving it. Question 1: In order to find out whether or not a driver’s education course enhances the scores on a driving examination, a sample of 6 students were provided the examination before and after taking the course. The outcomes are illustrated. a) Provide the hypotheses for problem. b) Calculate the test statistic. c) At 95% confidence, test the hypotheses. Test to see if taking the course in reality increased scores on driving examination. Question 2: In order to find out whether or not the number of automobiles sold per day (y) is associated to price (x1 in $1,000), and the number of advertising spots (x2), data was collected for 7 days: (data illustrated) a) Find out the least squares regression function associating y to x1 and x2.