Math 10 Exam 4 PLS SHOW WORK and ANSWER ALL THE QUESTIONS ---- NO EXCEPTION) (NOTE: your answer should be among the multiple choice questions/ answer if it's it means your is wrong so pls do your correctly and carefully!!!!!) NO MADE UP ANSWERS PLS AND THANK YOU!!!!!)

For Questions 9 - 30, use the pdf file Exam 4 - ANOVA and Regression Excel output

Question 1

In a study of the caffeine content for two brands of cola, the following table was obtained.

Brand A	Brand B
x1= 20.24	x2= 18.79
= 1.67	= 1.55
n1= 37	n2= 35

Construct a 90% confidence interval for?₁-?₂, the difference between the mean caffeine content for Brand A and the mean caffeine content for Brand B.

A.) 0.86 ?₁-?₂

B.) 0.68 ?₁-?₂

C.) 0.71 ?₁-?₂

D.) 0.96 ?₁-?₂

E.) 0.82 ?₁-?₂

Question 2

A researcher wishes to test whether the proportions of college students that transfer to an in-state university are the same for different colleges. She randomly selects 100 students from each college and records the number that transferred. The results are shown below.

?	College A	College B	College C	College D	College E
Transferred	85	74	76	84	88
Did not transfer	15	26	24	16	12

Suppose the test statistic value for a chi-square homogeneity of proportions test for this data is ?² = 9.722. Using ? = 0.05, are the proportions of students that transfer the same for all five colleges?

A.) H₀ is rejected. The proportions are the same for all five colleges

B.) H₀ is not rejected. The proportions are not the same for all five colleges

C.) H₀ is rejected. The proportions are not the same for all five colleges

D.) H₀ is not rejected. The proportions are the same for all five colleges

Question 3

A study compares employee satisfaction with respect to working conditions at two different facilities. At the first facility, a survey of 250 employees indicated 175 were satisfied with the working conditions. At the second facility, a survey of 320 employees indicated 216 were satisfied with the working conditions. Construct a 99% confidence interval for the difference between the true proportions of employee satisfaction at the two facilities.

A.) -0.052 p₁ - p₂

B.) -0.025 p₁ - p₂

C.) -0.076 p₁ - p₂

D.) -0.066 p₁ - p₂

E.) -0.039 p₁ - p₂

Question 4

A test of the hypothesesversusis made using the sample data shown below. Assume the two samples were taken from two normally distributed populations having the same population variance of 1.5. Find theP-value for the test.

n1= 50 n2= 40

x1= 66.32x2= 65.7

A.) 0.0588

B.) 0.0104

C.) 0.0294

D.) 0.0398

E.) 0.0208

Question 5

In an exit poll, 61 of 85 men sampled supported a ballot initiative to raise the local sales tax to fund a new hospital. In the same poll, 64 of 77 women sampled supported the initiative. Compute the test statistic value for testing whether the proportions of men and women who support the initiative are different.

A.) -1.69

B.) -1.63

C.) -1.75

D.) -1.66

E.) -1.72

Question 6

Many track runners believe that they have a better chance of winning if they start in the inside lane that is closest to the field. For the data below, the lane closest to the field is Lane 1, the next lane is Lane 2, and so on until the outermost lane, Lane 6. The table displays the starting positions (i.e., lane) for the winnners of 250 competitions. Is there sufficient evidence to conclude that wins are not evenly distributed among the six starting positions? Compute the test statistic value for a test of this claim.

Starting Position	1	2	3	4	5	6
Number of Wins	35	48	50	44	37	36

A.) 5.12

B.) 6.03

C.) 5.46

D.) 6.27

E.) 6.35

Question 7

Seven randomly selected plants that bottle the same beverage implemented a time management program in hopes of improving productivity. The average time, in minutes, that it took the companies to produce the same quantity of bottles before and after the program are shown below. Do the data support the conclusion that the program works? Compute the test statistic value for a test of the claim.

Before	75	89	31	90	120	50	40
After	70	80	30	85	100	49	42

A.) 3.354

B.) 1.767

C.) 4.328

D.) 2.019

E.) 5.571

Question 8

A study of 500 movie theater customers examined the snack purchasing habits for various movie types. The results are shown below. Calculate the test statistic value for testing whether snack purchasing habit is independent of movie type.

?	Action	Comedy	Horror
Snacks purchased	50	120	45
Snacks not purchased	75	175	35

A.) 6.55

B.) 6.73

C.) 6.39

D.) 6.84

E.) 6.27

Question 9

What is the ANOVA F test statistic value?

A.) 50.706

B.) 3.276

C.) 34

D.) 6.265

E.) 36

Question 10

What is the critical value for the test?

A.) 50.706

B.) 6.265

C.) 3.276

D.) 34

E.) 36

Question 11

What is the P-value for the test?

A.) 50.706

B.) 3.276

C.) 0.0000000000627

D.) 6.265

E.) 0.627

Question 12

Is the null hypothesis rejected?

A.) Yes

B.) No

Question 13

What is the conclusion for the test?

A.) The average horsepower is the same for all three types of cars.

B.) The average horsepower is not the same for all three types of cars.

Question 14

Which phrase best describes the relationship between the two variables?

A.) no discernable relationship

B.) nonlinear (curvilinear) relationship

C.) positive linear relationship

D.) negative linear relationship

Question 15

What is the value of the coefficient of determination?

A.) 0.634

B.) 0.692

C.) 0.479

D.) 0.832

E.) 0.476

Question 16

What is the value of the sample correlation coefficient?

A.) 0.479

B.) 0.692

C.) -0.692

D.) 0.476

E.) -0.479

Question 17

What is the sample size?

A.) 190

B.) 186

C.) 187

D.) 189

E.) 188

Question 18

What is the explanatory variable?

A.) condition

B.) age

Question 19

What is the response variable?

A.) age

B.) condition

Question 20

What is the test statistic value for the hypothesis test concerning the existence of a linear relationship between the two variables?

A.) -13.150

B.) 6.226

C.) -0.0213

D.) 69.655

E.) 0.0016

Question 21

What is the P-value for the hypothesis test concerning the existence of a linear relationship between the two variables?

A.) 0.01 P-value

B.) P-value

C.) P-value > 0.10

D.) 0.05 P-value

Question 22

What is the conclusion for the hypothesis test concerning the existence of a linear relationship between the two variables?

A.) Cannot be determined.

B.) A linear relationship exists.

C.) No linear relationship exists.

D.) A nonlinear (curvilinear) relationship exits.

Question 23

What percentage of the variation in the observed conditions of the bridges is explained by a linear relationship between age and condition?

A.) 69.2%

B.) 47.9%

C.) 83.2%

D.) 63.4%

E.) 95.0%

Question 24

What is the linear regression equation?

A.) y' = 6.226 + 0.0894x

B.) y' = -0.0213 + 0.0016x

C.) y' = 6.226 - 0.0213x

D.) y' = -0.0213 + 6.226x

Question 25

What is the estimated standard deviation for the residuals (i.e., s_est ) ?

A.) 0.692

B.) 0.634

C.) 0.0016

D.) 0.0894

E.) 0.476

Question 26

What condition does the linear regression model predict for an age of 44.38 years?

A.) 5.56

B.) 4.17

C.) 3.93

D.) 4.79

E.) 5.28

Question 27

What is the residual that corresponds to the observed data point (44.38, 4.55)?

A.) 0.73

B.) -0.73

C.) -0.24

D.) -0.62

E.) 0.62

Question 28

What is the 95% confidence interval for the slope of the regression line?

A.) (-0.0213, 0.0016)

B.) (-13.150, 69.655)

C.) (6.049, 6.402)

D.) (-0.0245, -0.0181)

Question 29

What is the meaning of the slope estimate b = -0.0213 as it relates age to condition?

A.) For every increase of 10 years in age, condition increases by 0.213.

B.) For every increase of 10 years in age, condition decreases by 2.13.

C.) For every increase of 10 years in age, condition decreases by 0.213.

D.) For every increase of 10 years in age, condition decreases by 0.0213.

E.) For every increase of 10 years in age, condition increases by 2.13.

Question 30

What does the linear regression model predict would be the change in condition given an increase in age of 50 years?

A.) about 1.06 higher

B.) about 1.6 lower

C.) about 1.6 higher

D.) about 0.6 lower

E.) about 1.06 lower

The New York State Department of Transportation (NYSDOT) inspects all bridges in the state every two years. Bridges are analyzed for their capacity to carry vehicular loads. Inspectors are required to evaluate and assign a condition score. The NYSDOT condition rating scale ranges from I to 7, with 7 being in new condition and a rating of 5 or greater considered as good condition. Based upon inspection and load capacity analysis, any bridge deemed unsafe gets closed. How does the condition of a bridge relate to its age at inspection? Use the Excel regression output shown here to answer questions 14 through 30. Condition as Age SUMMARY OUTPUT Condition (NYSDOT scale) Regression Statistics Multiple F 0.692187671 R Square 0.479123772 Adjusted R Square 0.476353154 Standard Error 0.634027562 40 100 120 Observations 190 Age (years) ANOVA df 55 MS Significance F Regression 1 69.51640535 69.51640535 172.9302749 1.97086E-28 Residual 188 75.57429846 0.401990949 Total 189 145.0907038 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 6.225677204 0.08937824 69.65540159 3.2797E-136 6.049364084 6.401990323 Age -0.021291198 0.001619066 -13.15029562 1.97086E-28 -0.024485069 -0.018097327A study was done on the average horsepower for 4-cylinder, 6-cylinder, and 8-cylinder cars, At a = 0,05, is the average horsepower the same for all three types? Use the Excel ANOVA output shown here to answer questions 9 through 13. SUMMARY Groups Count Sum Average Variance 4 cylinders 19 1545 81.31578947 223.3391813 6 cylinders 10 1114 111.4 189.3777778 8 cylinders 1104 138 110.2857143 ANOVA Source of Variation SS of MS F P-value F crit Between Groups 19377.22447 2 9688.612233 50.70615702 6.2654E-11 3.275897991 Within Groups 6496.505263 34 191.0736842 Total 25873.72973 36