HW 4 – Bus Stat
Directions: Choose the answer that best answers the question. Submit your solutions on a separate sheet.
1. The chi-square goodness of fit test will be valid if each of the expected cell frequencies is ______________.
A. Greater than 0
B. Less than 5
C. Between 0 and 5
D. At least 1
E. At least 5
2. The 2 statistic from a contingency table with 6 rows and five columns will have
A. 30 degrees of freedom
B. 24 degrees of freedom
C. 5 degrees of freedom
D. 20 degrees of freedom
E. 25 degrees of freedom
3. When we carry out a chi-square goodness of fit test for a normal distribution, the null hypothesis states that the
population:
A. Does not have a normal distribution
B. Has a normal distribution
C. Has a chi-square distribution
D. Does not have a chi-square distribution
E. Has k-3 degrees of freedom
4. A manufacturing company produces part 2205 for the aerospace industry. This particular part can be manufactured using
3 different production processes. The management wants to know if the quality of the units of part 2205 is the same for all
three processes. The production supervisor obtained the following data: The Process 1 had 29 defective units in 240 items;
Process 2 produced 12 defective units in 180 items and Process 3 manufactured 9 defective units in 150 items. At a
significance level of .05, the management wants to perform a hypothesis test to determine whether the quality of items
produced appears to be independent of the production process used. Calculate the expected number of conforming units
produced by Process 2.
A. 15.789
B. 168
C. 180
D. 164.211
E. 83.076
5. The chi-square goodness of fit test can be used when:
A. We conduct a binomial experiment
B. We conduct a multinomial experiment
C. We perform a hypothesis test to determine if a population has a normal distribution.
D. We perform a hypothesis test to determine if two population variances significantly differ from each other.
1
6. The ___________ the r2, and the __________ the s (standard error), the stronger the relationship between the dependent
variable and the independent variable.
A. Higher, lower
B. Lower, higher
C. Lower, lower
D. Higher, higher
7. A simple regression analysis with 20 observations would yield ________ degrees of freedom error and _________
degrees of freedom total.
A. 1, 20
B. 18, 19
C. 19, 20
D. 1, 19
E. 18, 20
8. The least squares regression line minimizes the sum of the
A. Differences between actual and predicted Y values
B. Absolute deviations between actual and predicted Y values
C. Absolute deviations between actual and predicted X values
D. Squared differences between actual and predicted Y values
E. Squared differences between actual and predicted X values
9.
The local grocery store wants to predict the daily sales in dollars. The manager believes that the amount of newspaper
advertising significantly affects the store sales. He randomly selects 7 days of data consisting of daily grocery store sales (in
thousands of dollars) and advertising expenditures (in thousands of dollars). The Excel/Mega-Stat output given above
summarizes the results of the regression model.
Determine a 95% confidence interval estimate of the daily average store sales based on $3000 advertising expenditures? The
distance value for this particular prediction is reported as .164.
A. $64,496 to $102.170
B. $33,108 to $133,558
C. $71,324 to $95,342
D. $51,314 to $115,353
E. $42,851 to $83,816
2
10. The simple linear regression (least squares method) minimizes:
A. The explained variation
B. SSyy
C. Total variation
D. SSxx
E. SSE
11.
The local grocery store wants to predict the daily sales in dollars. The manager believes that the amount of newspaper
advertising significantly affects the store sales. He randomly selects 7 days of data consisting of daily grocery store sales (in
thousands of dollars) and advertising expenditures (in thousands of dollars). The Excel/Mega-Stat output given above
summarizes the results of the regression model.
What is the value of the simple coefficient of determination?
A. 11.547
B. .762
C. .873
D. 6.6667
E. 1.6667
3
12.
The local grocery store wants to predict the daily sales in dollars. The manager believes that the amount of newspaper
advertising significantly affects the store sales. He randomly selects 7 days of data consisting of daily grocery store sales (in
thousands of dollars) and advertising expenditures (in thousands of dollars). The Excel/Mega-Stat output given above
summarizes the results of the regression model.
At a significance level of .05, test the significance of the slope and state your conclusion.
A. We reject H0 and conclude there is sufficient evidence that dollars spent on advertising is a useful linear predictor of the
grocery store sales.
B. We failed to reject H0 and conclude there is not sufficient evidence that dollars spent on advertising is a useful linear
predictor of the grocery store sales.
C. We failed to reject H0 and conclude there is sufficient evidence that dollars spent on advertising is a useful linear
predictor of the grocery store sales.
D. We reject H0 and conclude that there is sufficient evidence that grocery store sales in dollars is a useful linear predictor of
the dollars spent on advertising.
E. We reject H0 and conclude that there is not sufficient evidence that dollars spent on advertising is a useful linear predictor
of the grocery store sales.
4
13.
The local grocery store wants to predict the daily sales in dollars. The manager believes that the amount of newspaper
advertising significantly affects the store sales. He randomly selects 7 days of data consisting of daily grocery store sales (in
thousands of dollars) and advertising expenditures (in thousands of dollars). The Excel/Mega-Stat output given above
summarizes the results of the regression model.
In testing the population for significance at a significance level of .05, what is the rejection point condition for the two-sided
test?
A. Reject H0 if |t| > 2.571
B. Reject H0 if t > 2.571
C. Reject H0 if |t| < 2.571
D. Reject H0 if |t| > 2.051
E. Reject H0 if t > 2.051
14. The correlation coefficient may assume any value between
A. 0 and 1
B. - and 
C. 0 and 8
D. -1, and 1
E. -1, and 0
15. In a simple linear regression analysis, the correlation coefficient (a) and the slope (b) _____ have the same sign.
A. always
B. sometimes
C. never
16. For a given multiple regression model with three independent variables, the value of the adjusted multiple coefficient of
determination is _________ less than R2.
A. Always
B. Sometimes
C. Never
5
17. Adding any independent variable to a regression model will increase
A. Adjusted R2 or
B. s
C. MSE
D. R2
E. The length of all prediction intervals
18. A particular multiple regression model has 3 independent variables, the sum of the squared error is 7680, and the total
number of observations is 34. What is the value of the standard error of estimate?
A. 256
B. 232.72
C. 225.89
D. 16
E. 15.03
19. An investigator hired by a client suing for sex discrimination has developed a multiple regression model for employee
salaries for the company in question. In this multiple regression model, the salaries are in thousands of dollars. For example,
a data entry of 35 for the dependent variable indicates a salary of $35,000. The indicator (dummy) variable for gender is
coded as X1 = 0 if male and X1 = 1 if female. The computer output of this multiple regression model shows that the
coefficient for this variable (X1) is - 4.2. The t test showed that X1 was significant at  = 0.1. This result implies that for male
and female workers of the company,
A. On the average, females earn $4200 less.
B. On the average, males earn $4200 less.
C. On the average, salaries do not differ.
D. On the average, males have 4.2 more years of experience.
E. On the average, females have 4.2 more years of experience.
20. If it is desired to include marital status in a multiple regression model by using the categories: single, married, separated,
divorced, widowed, what will be the effect on the model?
A. One more independent variable will be included.
B. Two more independent variables will be included.
C. Three more independent variables will be included.
D. Four more independent variables will be included.
E. Five more independent variables will be included.
21. Which one of the following is not an assumption about the residuals in a regression model?
A. Constant variance
B. Independence
C. Normality
D. Variance of zero
E. Mean of zero
22. The chi-square goodness of fit is _________ a one-tailed test with the rejection region in the right tail.
A. Always
B. Sometimes
C. Never
6
23. The 2 statistic is used to test to test whether the assumption of normality is reasonable for a given population
distribution. The sample consists of 5000 observations and is divided into 6 categories (intervals). The degrees of freedom
for the chi-square statistic are:
A. 4999
B. 6
C. 5
D. 4
E. 3
7