Have good at statistics???

Q1:A computer used by a 24-hour banking service is supposed to randomly assign each transaction to one of 5 memory locations. A check at the end of a day's transactions gave the counts shown in the table to each of the 5 memory locations, along with the number of reported errors.

Memory Location: 1     2     3     4     5
Number of Transactions:    82   100 74   92   102
Number of Reported Errors      11   12   6     9     10


The bank manager wanted to test whether the proportion of errors in transactions assigned to each of the 5 memory locations differ. Referring to the table, which test would be used to properly analyze the data in this experiment?
Select one:

a.
chi-square test for independence in a two-way contingency table

b.
chi-square test for equal proportions in a one-way table

c.
ANOVA F test for main treatment effect

d.
Z test for the difference in two proportions


Q2 If we wish to determine whether there is evidence that the proportion of successes is higher in group 1 than in group 2, the appropriate test to use is
Select one:

a.
the Z test.

b.
the chi-squared test.

c.
the W test.

d.
the X test.

Q3 A candy bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses 6 small cities and offers the candy bar at different prices. Using candy bar sales as the dependent variable, the company will conduct a simple linear regression on the data below:

City Price ($) Sales
River Falls     1.30 100
Hudson  1.60 90
Ellsworth       1.80 90
Prescott 2.00 40
Rock Elm      2.40 38
Stillwater       2.90 32


Referring to the table, what is the coefficient of correlation for these data?
Select one:

a.
-0.8854

b.
-0.7839

c.
0.7839

d.
0.8854

Q4 If we use the chi-squared method of analysis to test for the differences among 4 proportions, the degrees of freedom are equal to:
Select one:

a.
3

b.
4

c.
5

d.
1

Q5
The following EXCEL output contains the results of a test to determine if the proportions of satisfied guests at two resorts are the same or different.

Hypothesized Difference 0
Level of Significance 0.05
Group 1
Number of Successes 163
Sample Size 227
Group 2
Number of Successes 154
Sample Size 262
Group 1 Proportion 0.718061674
Group 2 Proportion 0.58778626
Difference in Two Proportions 0.130275414
Average Proportion 0.648261759
Test Statistic 3.00875353
Two-Tailed Test
Lower Critical Value -1.959961082
Upper Critical Value 1.959961082
p-Value 0.002623357


Referring to the table, if you want to test the claim that "Resort 1 (Group 1) has a higher proportion of satisfied guests compared to Resort 2 (Group 2)," the p-value of the test will be
Select one:

a.
0.00262

b.
0.00262/2

c.
2*(0.00262)

d.
1 - (0.00262/2)

Q6 A buyer for a manufacturing plant suspects that his primary supplier of raw materials is overcharging. In order to determine if his suspicion is correct, he contacts a second supplier and asks for the prices on various materials. He wants to compare these prices with those of his primary supplier. The data collected is presented in the table below, with some summary statistics presented (all of these might not be necessary to answer the questions which follow). The buyer believes that the differences are normally distributed and will use this sample to perform an appropriate test at a level of significance of 0.01.

Material  Primary
Supplier Secondary
Supplier Difference
1     $55 $45 $10
2     $48 $47 $1
3     $31 $32 -$1
4     $83 $77 $6
5     $37 $37 $0
6     $55 $54 $1
Sum:      $309      $292      $17

Sum of Squares:  $17,573 $15,472 $139


Referring to the table, the test to perform is a
Select one:

a.
pooled-variance t test for differences in 2 means.

b.
separate-variance t test for differences in 2 means.

c.
Wilcoxon Rank Sum Test for differences in 2 medians.

d.
t-test for mean difference.

Q7 An economist is interested to see how consumption for an economy (in $ billions) is influenced by gross domestic product ($ billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.

SUMMARY OUTPUT

Regression Statistics
Multiple R     0.991
R Square      0.982
Adjusted R Square     0.976
Standard Error     0.299
Observations 10


ANOVA  df    SS  MS  F     Signif F
Regression   2     33.4163 16.7082 186.325 0.0001
Residual 7     0.6277   0.0897          
Total      9     34.0440              


Coeff     StdError t Stat      P-value
Intercept -0.0861  0.5674   -0.152    0.8837
GDP      0.7654   0.0574   13.340   0.0001
Price      -0.0006  0.0028   -0.219    0.8330


Referring to the tables, one economy in the sample had an aggregate consumption level of $4 billion, a GDP of $6 billion, and an aggregate price level of 200. What is the residual for this data point?
Select one:

a.
$4.39 billion

b.
$0.39 billion

c.
-$0.39 billion

d.
-$1.33 billion

Q8 Why would you use the Tukey-Kramer procedure?
Select one:

a.
To test for normality.

b.
To test for homogeneity of variance.

c.
To test independence of errors.

d.
To test for differences in pairwise means.

Q9 The Y-intercept (b0) represents the:
Select one:

a.
predicted value of Y when X = 0.

b.
change in estimated average Y per unit change in X.

c.
predicted value of Y.

d.
variation around the sample regression line.

Q10 A researcher randomly sampled 30 graduates of an MBA program and recorded data concerning their starting salaries. Of primary interest to the researcher was the effect of gender on starting salaries. Analysis of the mean salaries of the females and males in the sample is given below.

Size Mean     Std Dev
Females 18   48,266.7 13,577.63
Males     12   55,000   11,741.29
Std Error = 4,764.82
Means Diff = -6,733.3
Z = -1.4528 2-tailed p value = 0.1463
T = -1.4221 2-tailed p value = 0.1574

Referring to the table, the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates. What assumptions were necessary to conduct this hypothesis test?
Select one:

a.
Both populations of salaries (male and female) must have approximate normal distributions.

b.
The population variances are approximately equal.

c.
The samples were randomly and independently selected.

d.
All of the above assumptions were necessary.

Q11 Parents complain that children read too few storybooks and watch too µch television nowadays. A survey of 1,000 children reveals the following information on average time spent watching TV and average time spent reading storybooks

Average time spent reading storybooks
Average time
spent watching TV
Less than
1 hour
Between
1 and 2 hours
More than
2 hours
Less than 2 hours 90   85   130
More than 2 hours      655 32   8


Referring to the table, to test whether there is any relationship between average time spent watching TV and average time spent reading storybooks, the value of the measured test statistic is:
Select one:

a.
-12.59

b.
1.61

c.
481.49

d.
1,368.06

Q12 A manager of a product sales group believes the number of sales made by an employee (Y) depends on how many years that employee has been with the company (X1) and how he/she scored on a business aptitude test (X2). A random sample of 8 employees provides the following:

Employee     Y     X1   X2
1           100     10   7
2           90      3     10
3           80      8     9
4           70      5     4
5           60      5     8
6           50      7     5
7           40      1     4
8           30      1     1


Referring to the table, for these data, what is the estimated coefficient for the variable representing years an employee has been with the company, b1?
Select one:

a.
0.998

b.
3.103

c.
4.698

d.
21.293


Q13 The following EXCEL output contains the results of a test to determine if the proportions of satisfied guests at two resorts are the same or different.

Hypothesized Difference 0
Level of Significance 0.05
Group 1
Number of Successes 163
Sample Size 227
Group 2
Number of Successes 154
Sample Size 262
Group 1 Proportion 0.718061674
Group 2 Proportion 0.58778626
Difference in Two Proportions 0.130275414
Average Proportion 0.648261759
Test Statistic 3.00875353
Two-Tailed Test
Lower Critical Value -1.959961082
Upper Critical Value 1.959961082
p-Value 0.002623357

Referring to the data above, if you want to test the claim that "Resort 1 (Group 1) has a higher proportion of satisfied guests compared to Resort 2 (Group 2)," the p-value of the test will be
Select one:

a.
0.00262

b.
0.00262/2

c.
2*(0.00262)

d.
1 - (0.00262/2)

Q14 A realtor wants to compare the average sales-to-appraisal ratios of residential properties sold in four neighborhoods (W, X, Y, and Z). Four properties are randomly selected from each neighborhood and the ratios recorded for each, as shown below.

W: 1.2, 1.1, 0.9, 0.4
X: 2.5, 2.1, 1.9, 1.6
Y: 1.0, 1.5, 1.1, 1.3
Z: 0.8, 1.3, 1.1, 0.7


Interpret the results of the analysis summarized in the following table:

Source   df    SS  MS  F     PR > F
Neighborhoods           2.97 0.990     8.31 0.0260
Error      12                      
Total             4.40              


Referring to the table, the within group mean squares is
Select one:

a.
0.119

b.
0.990

c.
1.109

d.
8.31

Q15 If the p value is less than α in a two-tailed test,
Select one:

a.
the null hypothesis should not be rejected.

b.
the null hypothesis should be rejected.

c.
a one-tailed test should be used.

d.
no conclusion should be reached.

Q16 The following EXCEL output contains the results of a test to determine if the proportions of satisfied guests at two resorts are the same or different.

Hypothesized Difference 0
Level of Significance 0.05
Group 1
Number of Successes 163
Sample Size 227
Group 2
Number of Successes 154
Sample Size 262
Group 1 Proportion 0.718061674
Group 2 Proportion 0.58778626
Difference in Two Proportions 0.130275414
Average Proportion 0.648261759
Test Statistic 3.00875353
Two-Tailed Test
Lower Critical Value -1.959961082
Upper Critical Value 1.959961082
p-Value 0.002623357


Referring to the table, if you want to test the claim that "Resort 1 (Group 1) has a lower proportion of satisfied guests compared to Resort 2 (Group 2)," you will use
Select one:

a.
a t-test for the difference in two proportions.

b.
a z-test for the difference in two proportions.

c.
a chi-square test for the difference in two proportions.

d.
a chi-square test for independence.

Q17

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 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) = ß0 + ß1X

The results of the simple linear regression are provided below.

Y = -2,700+20X, syx = 65, two-tailed p value = 0.034 (for testing ß1)

Referring to the Table, interpret the p value for testing whether ß1 exceeds 0.
Select one:

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

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

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

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

Q18
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the µltiple regression. Microsoft Excel output is provided below:

SUMMARY OUTPUT

Regression Statistics
Multiple R     0.865
R Square      0.748
Adjusted R Square     0.726
Standard Error     5.195
Observations 50


ANOVA  df    SS  MS  F     Signif F
Regression          3605.7736    901.4434             0.0001
Residual       1214.2264    26.9828        
Total      49   4820.0000                  


Coeff     StdError t Stat      P-value
Intercept -1.6335  5.8078   -0.281    0.7798
Income  0.4485   0.1137   3.9545   0.0003
Size 4.2615   0.8062   5.286     0.0001
School   -0.6517  0.4319   -1.509    0.1383


Referring to the tables, one individual in the sample had an annual income of $10,000, a family size of 1, and an education of 8 years. This individual owned a home with an area of 1,000 square feet (House = 10.00). What is the residual (in hundreds of square feet) for this data point?
Select one:

a.
8.10

b.
5.40

c.
-5.40

d.
-8.10

Q19

A local real estate appraiser analyzed the sales prices of homes in 2 neighborhoods to the corresponding appraised values of the homes. The goal of the analysis was to compare the distribution of sale-to-appraised ratios from homes in the 2 neighborhoods. Random and independent samples were selected from the 2 neighborhoods from last year's homes sales, 8 from each of the 2 neighborhoods. Identify the nonparametric method that would be used to analyze the data.
Select one:

a.
the Wilcoxon Signed-Ranks Test, using the test statistic Z

b.
the Wilcoxon Signed-Ranks Test, using the test statistic W

c.
the Wilcoxon Rank Sum Test, using the test statistic T1

d.
the Wilcoxon Rank Sum Test, using the test statistic Z

Q20
One criterion used to evaluate employees in the assembly section of a large factory is the number of defective pieces per 1,000 parts produced. The quality control department wants to find out whether there is a relationship between years of experience and defect rate. Since the job is repetitious, after the initial training period any improvement due to a learning effect might be offset by a loss of motivation. A defect rate is calculated for each worker in a yearly evaluation. The results for 100 workers are given in the table below.

Years Since Training Period
< 1 Year 1 - 4 Years    5 - 9 Years
Defect Rate  High       6     9     9
Average 9     19   23
Low 7     8     10


Referring to the table, find the rejection region necessary for testing at the 0.05 level of significance whether there is a relationship between defect rate and years of experience.
Select one:

a.
Reject H0 if chi-square > 16.919

b.
Reject H0 if chi-square > 15.507

c.
Reject H0 if chi-square > 11.143

d.
Reject H0 if chi-square > 9.488

Q21
The Journal of Business Venturing reported on the activities of entrepreneurs during the organization creation process. As part of a designed study, a total of 71 entrepreneurs were interviewed and divided into 3 groups: those that were successful in founding a new firm (n1 = 34), those still actively trying to establish a firm (n2 = 21), and those who tried to start a new firm but eventually gave up (n3 = 16). The total number of activities undertaken (e.g., developed a business plan, sought funding, looked for facilities) by each group over a specified time period during organization creation was measured. The objective is to compare the mean number of activities of the 3 groups of entrepreneurs. Because of concerns over necessary assumption of the parametric analysis, it was decided to use a nonparametric analysis. Identify the nonparametric method that would be used to analyze the data.
Select one:

a.
Wilcoxon Rank Sums Test

b.
Wilcoxon Signed Rank Test

c.
Kruskal-Wallis Rank Test for Differences in Medians

d.
One-way ANOVA F test

Q22
Testing for the existence of correlation is equivalent to
Select one:

a.
testing for the existence of the slope (β1).

b.
testing for the existence of the Y-intercept (β0).

c.
the confidence interval estimate for predicting Y.

d.
testing for the existence of the slope (β10).

Q23

To test the effects of a business school preparation course, 8 students took a general business test before and after the course. The results are given below.

Student  Exam Score Before Course      Exam Score After Course
1     530 670
2     690 770
3     910 1,000
4     700 710
5     450 550
6     820 870
7     820 770
8     630 610


Referring to the table, at the 0.05 level of significance, the conclusion for this hypothesis test would be:
Select one:

a.
the business school preparation course does improve exam score.

b.
the business school preparation course does not improve exam score.

c.
the business school preparation course has no impact on exam score.

d.
It cannot be drawn from the information given.


Q24

A researcher randomly sampled 30 graduates of an MBA program and recorded data concerning their starting salaries. Of primary interest to the researcher was the effect of gender on starting salaries. Analysis of the mean salaries of the females and males in the sample is given below.

Size Mean     Std Dev
Females 18   48,266.7 13,577.63
Males     12   55,000   11,741.29
Std Error = 4,764.82
Means Diff = -6,733.3
Z = -1.4528 2-tailed p value = 0.1463
T = -1.4221 2-tailed p value = 0.1574

Referring to the table, the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates. According to the test run, which of the following is an appropriate alternative hypothesis?
Select one:

a.
H1: μfemales > μmales

b.
H1: μfemales < μmales

c.
H1: μfemales ≠ μmales

d.
H1: μfemales = μmales

Q25

A ____________ is a numerical quantity computed from the data of a sample and is used in reaching a decision on whether or not to reject the null hypothesis.
Select one:

a.
significance level

b.
critical value

c.
test statistic

d.
parameter

Q26

In a multiple regression model, the adjusted r2
Select one:

a.
cannot be negative.

b.
can sometimes be negative.

c.
can sometimes be greater than +1.

d.
has to fall between 0 and +1.


Q27

As a business statistics project, a student examined the factors that determine parking meter rates throughout the campus and downtown area. The campus is a group of buildings located in the center of downtown, with an open central quadrangle. Data were collected for the price of parking per hour and the number of blocks to the quadrangle. In addition, two dummy variables were coded to indicate the location of the parking meter (See below). The population regression model hypothesized is

Yi = ß0 + ß1x1i + ß2x2i + ß3x3i + ei

where
Y is the price per hour
x1 is a numerical variable = the number of blocks to the quadrangle
(Note that if x1 is less than 2, then the meter is on campus; if x1 is less than 3, then the meter is downtown)
x2 is a dummy variable = 1 if inside downtown and off campus, 0 otherwise
x3 is a dummy variable = 1 if outside downtown and off campus, 0 otherwise

The following Excel results are obtained.

Regression Statistics
Multiple R     9.9659
R Square      0.9331
Adjusted R Square     0.9294
Standard Error     0.0327
Observations 58


ANOVA  df    SS  MS  F     Signif F
Regression   3     0.8094   0.2698   251.1995      1.0964E-31
Residual 54   0.0580   0.0010          
Total      57   0.8675                


Coeff     StdError t Stat      P-value
Intercept 0.5118   0.0136   37.4675 2.4904
X1   -0.0045  0.0034   -1.3275  0.1898
X2   -0.2392  0.0123   -19.3942 5.3581E-26
X3   -0.0002  0.0123   -0.0214  0.9829


Referring to the tables, predict the meter rate per hour if one parks outside of downtown and off campus, 3 blocks from the quad.
Select one:

a.
$-0.0139

b.
$0.2589

c.
$0.2604

d.
$0.4981

Q28
If the Type I error (α) for a given test is to be decreased, then for a fixed sample size n
Select one:

a.
the Type II error (β) will also decrease.

b.
the Type II error (β) will increase.

c.
the power of the test will increase.

d.
a one-tailed test must be utilized.

Q29

If we are performing a two-tailed test of whether μ = 100, the probability of detecting a shift of the mean to 105 will be ________ the probability of detecting a shift of the mean to 110.
Select one:

a.
less than

b.
greater than

c.
equal to

d.
not comparable to

Q30

In testing for differences between the means of 2 independent populations, the null hypothesis is:
Select one:

a.
H0: μ1 - μ2 = 2.

b.
H0: μ1 - μ2 = 0.

c.
H0: μ1 - μ2 > 0.

d.
H0: μ1 - μ2 < 2.

Q31

Psychologists have found that people are generally reluctant to transmit bad news to their peers.
This phenomenon has been termed the "MM effect." To investigate the cause of the MM effect, 40 undergraduates at Duke University participated in an experiment. Each subject was asked to administer an IQ test to another student and then provide the test taker with his or her percentile score. Unknown to the subject, the test taker was a bogus student who was working with the researchers. The experimenters manipulated two factors: subject visibility and success of test taker, each at two levels. Subject visibility was either visible or not visible to the test taker. Success of the test taker was either visible or not visible to the test taker. Success of the test taker was either top 20% or bottom 20%. Ten subjects were randomly assigned to each of the 2 x 2 = 4 experimental conditions, then the time (in seconds) between the end of the test and the delivery of the percentile score from the subject to the test taker was measured. (This variable is called the latency to feedback.) The data were subjected to appropriate analyses with the following results.

Source   df    SS  MS  F     PR > F
Subject visibility    1     1380.24 1380.24 4.26 0.043
Test taker success      1     1325.16 1325.16 4.09 0.050
Interaction    1     3385.80 3385.80 10.45     0.002
Error      36   11,664.00     324.00          
Total      39   17,755.20                  


Referring to the table, in the context of this study, interpret the statement: "Subject visibility and test taker success interact."
Select one:

a.
The difference between the mean feedback time for visible and nonvisible subjects depends on the success of the test taker.

b.
The difference between the mean feedback time for test takers scoring in the top 20% and bottom 20% depends on the visibility of the subject.

c.
The relationship between feedback time and subject visibility depends on the success of the test taker.

d.
All of the above are correct interpretations

Q32

A researcher randomly sampled 30 graduates of an MBA program and recorded data concerning their starting salaries. Of primary interest to the researcher was the effect of gender on starting salaries. Analysis of the mean salaries of the females and males in the sample is given below.

Size Mean     Std Dev
Females 18   48,266.7 13,577.63
Males     12   55,000   11,741.29
Std Error = 4,764.82
Means Diff = -6,733.3
Z = -1.4528 2-tailed p value = 0.1463
T = -1.4221 2-tailed p value = 0.1574

Referring to the table, the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates. From the analysis in the table, the correct test statistic is:
Select one:

a.
4,634.72

b.
-1.4221

c.
-1.4528

d.
-6,733.33

Q33

A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this µltiple regression.

SUMMARY OUTPUT

Regression Statistics
Multiple R     0.830
R Square      0.689
Adjusted R Square     0.662
Standard Error     17501.643
Observations 26


ANOVA  df    SS  MS  F     Signif F
Regression   2     15579777040       7789888520  25.432   0.0001
Residual 23   7045072780  306307512          
Total      25   22624849820                    


Coeff     StdError t Stat      P-value
Intercept 15800.0000   6038.2999    2.617     0.0154
Capital   0.1245   0.2045   0.609     0.5485
Wages   7.0762   1.4729   4.804     0.0001


Referring to the tables, which of the following values for a is the smallest for which the regression model as a whole is significant?
Select one:

a.
15,800.00

b.
16,520.07

c.
17,277.49

d.
20,455.98

Q34

If a test of hypothesis has a Type I error probability (α) of 0.01, we mean
Select one:

a.
if the null hypothesis is true, we don't reject it 1% of the time.

b.
if the null hypothesis is true, we reject it 1% of the time.

c.
if the null hypothesis is false, we don't reject it 1% of the time.

d.
if the null hypothesis is false, we reject it 1% of the time.

Q35

A study published in the American Journal of Public Health was conducted to determine whether the use of seat belts in motor vehicles depends on ethnic status in San Diego County. A sample of 792 children treated for injuries sustained from motor vehicle accidents was obtained, and each child was classified according to (1) ethnic status (Hispanic or non-Hispanic) and (2) seat belt usage (worn or not worn) during the accident. The number of children in each category is given in the table below.

Hispanic Non-Hispanic
Seat belts worn    31   148
Seat belts not worn     283 330


Referring to the table, which test would be used to properly analyze the data in this experiment?
Select one:

a.
chi-square test for independence in a two-way contingency table.

b.
chi-square test for equal proportions in a one-way table.

c.
ANOVA F test for interaction in a 2 x 2 factorial design.

d.
chi-square test for a 2 x 2 factorial design.

Q36

If a group of independent variables are not significant individually but are significant as a group at a specified level of significance, this is most likely due to:
Select one:

a.
autocorrelation.

b.
the presence of dummy variables.

c.
the absence of dummy variables.

d.
collinearity.

Q37

A campus researcher wanted to investigate the factors that affect visitor travel time in a complex, multilevel building on campus. Specifically, he wanted to determine whether different building signs (building maps versus wall signage) affect the total amount of time visitors require to reach their destination and whether that time depends on whether the starting location is inside or outside the building. Three subjects were assigned to each of the combinations of signs and starting locations, and travel time in seconds from beginning to destination was recorded. How should the data be analyzed?

     Starting Room
     Interior   Exterior
Wall Signs    141 224
119 339
238 139
Map 85   226
94   129
126 130
Select one:

a.
Completely randomized design

b.
Randomized block design

c.
2 x 2 factorial design

d.
Kruskal-Wallis rank test

Q38

The sample correlation coefficient between X and Y is 0.375. It has been found out that the p-value is 0.256 when testing H0: ρ = 0 against the two-sided alternative H1: ρ ≠ 0. To test H0: ρ = 0 against the one-sided alternative H1: ρ > 0 at a significance level of 0.193, the p-value is
Select one:

a.
0.256/2

b.
0.256

c.
1 - 0.256

d.
1 - 0.256/2


Q39

A manager of a product sales group believes the number of sales made by an employee (Y) depends on how many years that employee has been with the company (X1) and how he/she scored on a business aptitude test (X2). A random sample of 8 employees provides the following:

Employee     Y     X1   X2
1     100 10   7
2     90   3     10
3     80   8     9
4     70   5     4
5     60   5     8
6     50   7     5
7     40   1     4
8     30   1     1


Referring to the table, what is the estimated coefficient for the variable representing scores on the aptitude test, b2?
Select one:

a.
0.998

b.
3.103

c.
4.698

d.
21.293

Q40

In testing for the differences between the means of 2 independent populations where the variances in each population are unknown but assumed equal, the degrees of freedom are
Select one:

a.
n - 1.

b.
n1 + n2 - 1.

c.
n1 + n2 - 2.

d.
n - 2.