# 20 Business Statistics Questions

Please see attached file to view the tables.

1. The Y-intercept (b0) represents the

A) variation around the sample regression line.

B) predicted value of Y when X = 0.

C) predicted value of Y.

D) change in estimated average Y per unit change in X.

2. The slope (b1) represents the

A) predicted value of Y when X = 0.

B) estimated average change in Y per unit change in X.

C) variation around the line of regression.

D) predicted value of Y.

3. The least squares method minimizes which of the following?

A) SST

B) SSE

C) SSR

D) all of the above

4. The standard error of the estimate is a measure of the

A) explained variation.

B) variation of the X variable.

C) total variation of the Y variable.

D) variation around the sample regression line.

5.

TABLE 13-1

A large national bank charges local companies for using their services. A bank official reported the results of a regression analysis designed to predict the bank's charges (Y)-measured in dollars per month-for services rendered to local companies. One independent variable used to predict the service charge to a company is the company's sales revenue (X)-measured in millions of dollars. Data for 21 companies who use the bank's services were used to fit the model:

E(Y) = b0 + b1X

The results of the simple linear regression are provided below.

Y= -2,700 + 20X, SYX = 65, two-tailed p value = 0.034 (for testing b1)

Referring to Table 13-1, interpret the estimate of b0, the Y-intercept of the line.

A) There is no practical interpretation since a sales revenue of $0 is a nonsensical value.

B) All companies will be charged at least $2,700 by the bank.

C) About 95% of the observed service charges fall within $2,700 of the least squares line.

D) For every $1 million increase in sales revenue, we expect a service charge to decrease $2,700.

6.

TABLE 13-1

A large national bank charges local companies for using their services. A bank official reported the results of a regression analysis designed to predict the bank's charges (Y)-measured in dollars per month-for services rendered to local companies. One independent variable used to predict the service charge to a company is the company's sales revenue (X)-measured in millions of dollars. Data for 21 companies who use the bank's services were used to fit the model:

E(Y) = b0 + b1X

The results of the simple linear regression are provided below.

Y = -2,700 + 20X, SYX = 65, two-tailed p value = 0.034 (for testing b1)

Referring to Table 13-1, interpret the estimate of the standard deviation of the random error term (standard error of the estimate) in the model.

A) About 95% of the observed service charges equal their corresponding predicted values.

B) About 95% of the observed service charges fall within $65 of the least squares line.

C) For every $1 million increase in sales revenue, we expect a service charge to increase $65.

D) About 95% of the observed service charges fall within $130 of the least squares line.

7.

TABLE 13-1

A large national bank charges local companies for using their services. A bank official reported the results of a regression analysis designed to predict the bank's charges (Y)-measured in dollars per month-for services rendered to local companies. One independent variable used to predict the service charge to a company is the company's sales revenue (X)-measured in millions of dollars. Data for 21 companies who use the bank's services were used to fit the model:

E(Y) = b0 + b1X

The results of the simple linear regression are provided below.

Y = -2,700 + 20X, SYX = 65, two-tailed p value = 0.034 (for testing b1)

Referring to Table 13-1, interpret the p value for testing whether b1 exceeds 0.

A) For every $1 million increase in sales revenue, we expect a service charge to increase $0.034.

B) Sales revenue (X) is a poor predictor of service charge (Y).

C) There is sufficient evidence (at the alpha = 0.05) to conclude that sales revenue (X) is a useful linear predictor of service charge (Y).

D) There is insufficient evidence (at the alpha = 0.10) to conclude that sales revenue (X) is a useful linear predictor of service charge (Y).

8.

TABLE 13-1

E(Y) = b0 + b1X

The results of the simple linear regression are provided below.

Y= -2,700 + 20X, SYX = 65, two-tailed p value = 0.034 (for testing b1)

Referring to Table 13-1, a 95% confidence interval for b1 is (15, 30). Interpret the interval.

A) We are 95% confident that the sales revenue (X) will increase between $15 and $30 million for every $1 increase in service charge (Y).

B) At the alpha = 0.05 level, there is no evidence of a linear relationship between service charge (Y) and sales revenue (X).

C) We are 95% confident that the mean service charge will fall between $15 and $30 per month.

D) We are 95% confident that average service charge (Y) will increase between $15 and $30 for every $1 million increase in sales revenue (X).

9.

TABLE 13-3

The director of cooperative education at a state college wants to examine the effect of cooperative education job experience on marketability in the work place. She takes a random sample of 4 students. For these 4, she finds out how many times each had a cooperative education job and how many job offers they received upon graduation. These data are presented in the table below.

Referring to Table 13-3, the least squares estimate of the slope is ________.

10.

TABLE 13-3

The director of cooperative education at a state college wants to examine the effect of cooperative education job experience on marketability in the work place. She takes a random sample of 4 students. For these 4, she finds out how many times each had a cooperative education job and how many job offers they received upon graduation. These data are presented in the table below.

Referring to Table 13-3, the least squares estimate of the Y-intercept is ________.

11.

TABLE 13-3

The director of cooperative education at a state college wants to examine the effect of cooperative education job experience on marketability in the work place. She takes a random sample of 4 students. For these 4, she finds out how many times each had a cooperative education job and how many job offers they received upon graduation. These data are presented in the table below.

Referring to Table 13-3, the prediction for the number of job offers for a person with 2 co-op jobs is ________.

12.

TABLE 13-3

Referring to Table 13-3, the total sum of squares (SST) is ________.

13.

TABLE 13-3

Referring to Table 13-3, the regression sum of squares (SSR) is ________.

14.

TABLE 13-3

Referring to Table 13-3, the error or residual sum of squares (SSE) is ________.

15.

TABLE 13-3

Referring to Table 13-3, the coefficient of determination is ________.

16.

TABLE 13-3

Referring to Table 13-3, the standard error of estimate is ________.

17.

TABLE 13-3

Referring to Table 13-3, the coefficient of correlation is ________.

18.

TABLE 13-3

Referring to Table 13-3, suppose the director of cooperative education wants to obtain a 95% confidence-interval estimate for the mean number of job offers received by people who have had exactly one cooperative education job. The t critical value she would use is ________.

19.

TABLE 13-3

Referring to Table 13-3, suppose the director of cooperative education wants to obtain a 95% confidence interval estimate for the mean number of job offers received by people who have had exactly one cooperative education job. The confidence interval is from ________ to ________.

20.

TABLE 13-3

Referring to Table 13-3, suppose the director of cooperative education wants to obtain a 95% prediction interval estimate for the mean number of job offers received by people who have had exactly one cooperative education job. The prediction interval is from ________ to ________.

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Practice Questions with Statistics

5. A political polling company wants to know if there are differences among people of different political parties with respect to their views on a bill recently proposed in Congress. The company conducted a survey of 300 people and got the following results. Do the results support the hypothesis that there are differences among people in different political parties regarding their views on this bill? (Use a = 0.10)

Republicans Democrats Independents

Strongly Agree 50 10 20

Agree 20 10 15

Neutral 20 20 10

Disagree 10 35 20

Strongly Disagree 10 30 20

15. A researcher in a private, for-profit university wants to determine whether the average starting salaries differ among recent graduates from their nursing, engineering, business and education programs. He randomly selects graduates from each of these programs and determines their starting salaries (see table below). Is there a significant difference in starting salaries among the four programs? NOTE: values are in $1,000. (Use a = 0.05)

Nursing Engineering Business Education

42 51 60 54

44 49 62 48

47 55 59 49

39 54 61 50

44 58 58 51

46 58

11. A software company wants to know whether the job satisfaction levels of its programmers is linked to their salary levels. The company provides a written questionnaire to a sample of fifteen programmers to measure their job satisfaction levels on a scale of 1 to 10. The data are shown in the table below.

(a) Draw a scatter plot.

(b) Develop a regression equation relating job satisfaction to salary.

(c) Predict the job satisfaction rating for someone with a salary of $30,000.

Job Satisfaction (1-10): 1 2 2 3 3 5 6 6 7 7 8 8 9 9 10

Annual Salary (in $1000): 22 20 23 34 38 24 22 34 36 27 33 27 38 39 40

7. A fast-food company is trying to reduce the amount of time it takes to prepare its Jumbo-Max meal, which takes on average 4.2 minutes ( µ ) and the standard deviation of the population equals 0.8 minutes. The company hires a consultant who designs a new system for preparing the Jumbo-Max and the company uses the new system for a week. During that week, the company makes 64 Jumbo-Max meals and the mean time for the sample is 3.8 minutes. Is the consultant's new system effective in reducing the preparation time? (Use a = 0.01)

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