## Test to determine whether the population correlation coefficient is negative

1.You are given the following sample data for two variables:Y X

10 100

8 110

12 90

15 200

16 150

10 100

10 80

8 90

12 150

2.The regression model based on these sample data explains approximately 75 percent of the variation in the dependent variable.

True/False?

3.A manufacturing company is interested in predicting the number of defects that will be produced each hour on the assembly line. The managers believe that there is a relationship between the defect rate and the production rate per hour. The managers believe that they can use production rate to predict the number of defects. The following data were collected for 10 randomly selected hours.

Defects Production Rate Per Hour

20 400

30 450

10 350

20 375

30 400

25 400

30 450

20 300

10 300

40 300

4.Given these sample data, the simple linear regression model for predicting the number of defects is approximately = 5.67 + 0.048x.

True/False?

5.When constructing a scatter plot, the dependent variable is placed on the vertical axis and the independent variable is placed on the horizontal axis.

True/False?

6.A random sample of two variables, x and y, produced the following observations:

x y

19 7

13 9

17 8

9 11

12 9

25 6

20 7

17 8

Test to determine whether the population correlation coefficient is negative. Use a significance level of 0.05 for the hypothesis test.

A.Because t =-4.152 < -1.9432, reject the null hypothesis. Because the null hypothesis is rejected, the sample data does support the hypothesis that there is a negative linear relationship between x and y.

B.Because t =-4.152 < -1.9432, do not reject the null hypothesis. Because the null hypothesis is not rejected, the sample data support the hypothesis that there is a negative linear relationship between x and y.

C.Because t =-4.152 < -1.9432, do not reject the null hypothesis. Because the null hypothesis is not rejected, the sample data support the hypothesis that there is a negative linear relationship between x and y.

D.Because t =-9.895 < -1.9432, reject the null hypothesis. Because the null hypothesis is rejected, the sample data does support the hypothesis that there is a negative linear relationship between x and y.

You are given the following sample data for two variables:

Y X

10 100

8 110

12 90

15 200

16 150

10 100

10 80

8 90

12 150

7.The sample correlation coefficient for these data is approximately r = 0.755.

True/False?

8.Based upon these sample data, and testing at the 0.05 level of significance, the critical value for testing whether the population correlation coefficient is equal to zero is t = 2.2622.

True/False?

9.The following regression model has been computed based on a sample of twenty observations: = 34.2 + 19.3x. Given this model, the predicted value for y when x =40 is 806.2.

True/False?

10.When a correlation is found between a pair of variables, this always means that there is a direct cause and effect relationship between the variables.

True/False?

11.State University recently randomly sampled ten students and analyzed grade point average (GPA) and number of hours worked off-campus per week. The following data were observed:

GPA HOURS

3.14 25

2.75 30

3.68 11

3.22 18

2.45 22

2.80 40

3.00 15

2.23 29

3.14 10

2.90 0

The correlation between these two variables is approximately -.461

True/False?

12.In a university statistics course a correlation of -0.8 was found between numbers of classes missed and course grade. This means that the fewer classes students missed, the higher the grade.

True/False?

13.Two variables have a correlation coefficient that is very close to zero. This means that there is no relationship between the two variables.

True/False?

14.The following regression model has been computed based on a sample of twenty observations: = 34.2 + 19.3x. The first observations in the sample for y and x were 300 and 18, respectively. Given this, the residual value for the first observation is approximately 81.6.

True/False?

15.A bank is interested in determining whether its customers’ checking balances are linearly related to their savings balances. A sample of n = 20 customers was selected and the correlation was calculated to be +0.40. If the bank is interested in testing to see whether there is a significant linear relationship between the two variables using a significance level of 0.05, the value of the test statistic is approximately t =1.8516.

true/False?

16.A correlation of -0.9 indicates a weak linear relationship between the variables.

True/False?

17.If the correlation between two variables is known to be statistically significant at the 0.05 level, then the regression slope coefficient will also be significant at the 0.05 level.

True/False?

18.An industry study was recently conducted in which the sample correlation between units sold and marketing expenses was 0.57. The sample size for the study included 15 companies. Based on the sample results, test to determine whether there is a significant positive correlation between these two variables. Use an alpha = 0.05

A.Because t = 2.50 > 1.7709, reject the null hypothesis. There is sufficient evidence to conclude there is a positive linear relationship between sales units and marketing expense for companies in this industry

B.Because t = 3.13 > 1.7709, reject the null hypothesis. There is sufficient evidence to conclude there is a positive linear relationship between sales units and marketing expense for companies in this industry.

C.Because t = 3.13 > 1.7709, reject the null hypothesis. There is sufficient evidence to conclude there is a positive linear relationship between sales units and marketing expense for companies in this industry.

D.Because t = 2.50 > 1.7709, do not reject the null hypothesis. There is not sufficient evidence to conclude there is a positive linear relationship between sales units and marketing expense for companies in this industry.

19.In developing a scatter plot, the decision maker has the option of connecting the points or not.

True/False?

20.If two variables are highly correlated, it not only means that they are linearly related, it also means that a change in one variable will cause a change in the other variable.

True/False?

21.A research study has stated that the taxes paid by individuals is correlated at a .78 value with the age of the individual. Given this, the scatter plot would show points that would fall on straight line on a slope equal to .78.

True/False?

22.A dependent variable is the variable that we wish to predict or explain in a regression model.

True/False?

23.If a set of data contains no values of x that are equal to zero, then the regression coefficient, b0, has no particular meaning.

True/False?

24.The scatter plot is a two dimensional graph that is used to graphically represent the relationship between two variables.

True/False?

25.The difference between a scatter plot and a scatter diagram is that the scatter plot has the independent variable on the x-axis while the independent variable is on the Y-axis in a scatter diagram.

True/False?

26.If a sample of n = 30 people is selected and the sample correlation between two variables is r = 0.468, what is the test statistic value for testing whether the true population correlation coefficient is equal to zero?

A.t = 2.0484

B.About t = 2.80

C.About t = -.3.01

D.Can’t be determined without knowing the level of significance for the test.

A study was recently done in which the following regression output was generated using Excel.

SUMMARY OUTPUT

27.Given this, we know that approximately 57 percent of the variation in the y variable is explained by the x variable.

True/False?

28.Given this output, the point estimate for the average tip per dollar amount of the bill is approximately $0.21.

True/False?

29.Given this output, we would reject the null hypothesis that the population regression slope coefficient is equal to zero at the alpha = 0.05 level.

True/False?