Reference no: EM13154854

T/F 
1. In a regression model, a value of the error term depends upon other values of the error term. 
False
2. In testing the difference between two means from two independent populations, the sample sizes do not have to be equal to be able to use the Z statistic.
True
3. The least squares simple linear regression line minimizes the sum squares of the vertical deviations between the line and the data points.
False
4. For a hypothesis test about a population proportion or mean, if the level of significance is less than the p-value, the null hypothesis is rejected.
False
5. The error term in the regression model describes the effects of all factors other than the independent variables on y (response variable).
6. You cannot make a Type II error when the null hypothesis is true.
True
7. In performing a chi-square test of independence, as the difference between the respective observed and expected frequencies decrease, the probability of concluding that the row variable is independent of the column variable increases. 
True
8. The chi-square distribution is a continuous probability distribution that is skewed to the left.
9. The larger the p-value, the more the chance of rejecting the null hypothesis. 
10. The error term is the difference between the observed value of the dependent variable and the predicted value of the dependent variable. 
11. A fastener manufacturing company uses a chi-square goodness of fit test to determine if a population of all lengths of ¼ inch bolts it manufactures is distributed according to a normal distribution. If we reject the null hypothesis, it is reasonable to assume that the population distribution is at least approximately normally distributed. 
12. The level of significance indicates the probability of rejecting a false null hypothesis. 
False
13. The correlation coefficient is the ratio of explained variation to total variation.
14. In a regression model, at any given combination of values of the independent variables, the population of potential error terms is assumed to have an F-distribution. 
False
Multiple choices 
1. When we carry out a chi-square test of independence, as the difference between the respective observed and expected frequencies decrease, the probability of concluding that the row variable is independent of the column variable: A. Decreases
B. Increases
C. May increase or decrease depending on the number of rows and columns
D. Will be unaffected
2. One survey conducted by a major leasing company determined that the Lexus is the favorite luxury car for 25% of leases in Atlanta. Suppose a US car manufacturer conducts its own survey in an effort to determine if this figure is correct. Of the 384 leases in Atlanta surveyed, 79 lease a Lexus. Calculate the appropriate test statistic to test the hypotheses.
A. -2.15
B. -2.00
C. -0.91
D. 2.00
E. 2.51
3. The changing ecology of the swamps in Louisiana has been the subject of much environmental research. One water-quality parameter of concern is the total phosphorous level. Suppose that the EPA makes 15 measurements in one area of the swamp, yielding a mean level of total phosphorus of 12.3 parts per billion (ppb) and a standard deviation of 5.4 ppb. The EPA wants to test whether the data support the conclusion that the mean level is less than 15 ppb. Calculate the appropriate test statistic to test the hypotheses. 
A. 7.50
B. 1.94
C. 3.88
D. -1.94
E. -7.50
4. Given the following information about a hypothesis test of the difference between two means based on independent random samples, what is the calculated value of the test statistic? Assume that the samples are obtained from normally distributed populations having equal variances. 
H1: mu1> mu2; Xbar1=12, Xbar2=9, s1 = 5, s2 = 3, n1 = 13, n2 = 10. 
A. t = 1.674
B. t = 1.501
C. t = 2.823
D. t = 1.063
5. A major airline company is concerned that its proportion of late arrivals has substantially increased in the past month. Historical data shows that on the average 18% of the company airplanes have arrived late. In a random sample of 1,240 airplanes, 310 airplanes have arrived late. If we are conducting a hypothesis test of a single proportion to determine if the proportion of late arrivals has increased: What is the value of the calculated test statistic? 
A. Z= 3.208
B. Z = 6.416
C. Z = -3.208
D. Z = -6.416
E. Z = 1.833
6. 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
D. Can be greater or less depending on the standard error
7. A manufacturer of a chemical used in glue, attempting to control the amount of a hazardous chemical its workers are exposed to, has given instructions to halt production if the mean amount in the air exceeds 3.0ppm. It is believed that the standard deviation is 0.5. ppm from a previous study. A random sample of 50 air specimens produced the sample mean=3.1 ppm. If the ? level of shutting down production is set at 0.05, given this air sample should production be halted?
A. No
B. Yes
C. Insufficient information to make a decision
D. Depends on the power of the test
8. The range of feasible values for the multiple coefficient of determination is from:
A. 0 to infinity
B. -1 to 0
C. -1 to 1
D. Any real value

9. 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
10. A manufacturing operation consists of a unique system that produces an average of 15.5 jet engine propulsion parts every hour. After undergoing a complete overhaul, the system was monitored by observing the number of parts produced in each of sixteen randomly selected one-hour periods. The mean is 15.42 with a standard deviation of 0.16. Calculate the appropriate test statistic to test the hypotheses. 
A. -8.00
B. -2.00
C. 8.00
D. 2.00
E. -0.50
11. A multiple regression analysis with 20 observations on each of three independent variables and the dependent variable would yield _____ and ______ degrees of freedom respectively for regression (explained) and error. 
A. 3, 17
B. 3, 16
C. 4, 16
D. 3, 19
E. 3, 20
12. A new company is in the process of evaluating its customer service. The company offers two types of sales: 1. Internet sales; 2. Store sales. The marketing research manager believes that the Internet sales are more than 10% higher than store sales. The null hypothesis would be:
A. Pinternet - Pstore > .10
B. Pinternet - Pstore < .10
C. Pinternet - Pstore >= .10
D. Pinternet - Pstore <= .10
E. Pinternet - Pstore = .10
13 If we are testing the significance of the independent variable X1 and we reject the null hypothesis H0: ?1 = 0, we conclude that:(Chs. 13 & 14)
A. X1 is significantly related to Y
B. X1 is not significantly related to Y
C. X1 is an unimportant independent variable
D. ?1 is significantly related to the dependent variable Y

14 A manufacturer of a chemical used in glue, attempting to control the amount of a hazardous chemical its workers are exposed to, has given instructions to halt production if the mean amount in the air exceeds 3.0ppm. A random sample of 50 air specimens produced the following statistics: sample mean=3.1 ppm , sample standard deviation=0.5 ppm. Calculate the appropriate test statistic to test the hypotheses.
A. 0.20
B. -0.20
C. 10.00
D. 1.41
E. -1.41

Essay type 
1. Consider the following partial computer output for a multiple regression model.
Predictor Coefficient Standard Deviation

Constant 41.225 6.380
X1 1.081 1.353
X2 -18.404 4.547

Analysis of Variance
Source DF SS
Regression 2 2270.11
Error 26 3585.75
What is the number of Observations in the sample? Write the least squares regression (prediction) equation. Test the usefulness of variable x2 in the model at alpha =.05. Calculate the t statistic and state your conclusions.
2. Historically the average age of European soccer players is reported as 26 years with a standard deviation of 4 years. A random sample of 81 European professional soccer players has an average age of 27 years. We would like to decide if there is enough evidence to establish that average age of European soccer players has increased significantly. What is the decision at ?=.05 and 0.01? Indicate which test you are performing; show the hypotheses, the test statistic and the critical values and mention whether one-tailed or two-tailed.(Ch9)
3. Test H0: mu=42 versus HA: mu is not equal to 42 when Xbar = 42.8, s=1.2 and n=16 at ?=.01 and .05. Assume that the population from which the sample is selected is normally distributed. Indicate which test you are performing; show the test statistic and the critical values and mention whether one-tailed or two-tailed.(Ch 9)
4. A recent study conducted by the state government attempts to determine whether the voting public supports further increase in cigarette taxes. The opinion poll recently sampled 1500 voting age citizens. 1020 of the sampled citizens were in favor of an increase in cigarette taxes. The state government would like to decide if there is enough evidence to establish whether the proportion of citizens supporting an increase in cigarette taxes is significantly greater than .66 at 5% and 10% significance levels. Indicate which test you are performing; show the hypotheses, the test statistic and the critical values and mention whether one-tailed or two-tailed. (Ch9)
5 A data set with 7 observations yielded the following. Use the simple linear regression model.
Greek letter Capital Sigma X =21.57
Greek letter Capital Sigma X2 =68.31
Greek letter Capital SigmaY =188.9
Greek letter Capital Sigma Y2 =5,140.23
Greek letter Capital Sigma XY =590.83
Write the Regression Equation showing Intercept and slope and test the significance of slope at 1% significance level.(Ch13)
6. A human resource manager is interested in whether absences occur during the week with equal frequency. The manager took a random sample of 100 absences and created the following table:

Monday 28
Tuesday 20
Wednesday 12
Thursday 18
Friday 22

At a significance level of alpha = .05 test the Null that the probabilities of absences are the same for all five days.
7. Test H0: pi1- pi2 ??.01, HA: pi1- pi2 > .01 at ????? =.05 where p1=.08, p2=.035, n1 = 200, n2 = 400. Indicate which test you are performing; show the test statistic and the critical values and mention whether one-tailed or two-tailed.
Note that pi stands for the Greek letter representing population proportion. 

8. A data set with 7 observations yielded the following. Use the simple linear regression model.
Greek letter Capital Sigma X =21.57
Greek letter Capital Sigma X2 =68.31
Greek letter Capital SigmaY =188.9
Greek letter Capital Sigma Y2 =5,140.23
Greek letter Capital Sigma XY =590.83
Calculate the Correlation coefficient, Coefficient of determination and SSE, and the Standard Error of Estimate.(Ch 13)
9. In an opinion survey, a random sample of 1000 adults from the U.S.A and 1000 adults from Germany were asked whether they supported the death penalty. 590 American adults and 560 German adults indicated that they supported the death penalty. The researcher wants to know if there is sufficient evidence to conclude that the proportion of adults who support the death penalty is higher in the U.S.A. than in Germany. What is the decision at alpha = 0.05 and 0.10 (Ch 10)
10. At a recent meeting of educational researchers comparison were made between the type of college freshmen attend and the numbers who drop out. A random sample of freshmen show the following results: (keep two decimals in calculating expected frequencies)
4Yr public 4Yr private 2Yr public 2Yr private
dropout 10 9 15 9
don't drop 26 28 18 27
Use a significance level of .05 and determine if the type of school and the dropout rate are independent. (Ch12)

11. Consider the following partial computer output for a multiple regression model.
Predictor Coefficient Standard Deviation

Constant 41.225 6.380
X1 1.081 1.353
X2 -18.404 4.547

Analysis of Variance
Source DF SS
Regression 2 2270.11
Error 26 3585.75
Find Total Sum of Squares, Explained Variation, SSE, MSE, R-Squared, and Test the overall usefulness of the model at 1% level of significance calculating the F-Statistic.