Final Exam Ch. 7 – 11, 13 – 14

Final Exam Ch. 7 – 11, 13 – 14
The next 7 questions refer to the following scenario. A long jump competition took place recently at a local high school. The coach is interested in performing as well as possible next time, so he is looking at the relationship between height and distance jumped (both measured in inches). Use height to predict distance.
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Regression Statistics
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R Square 0.9819
Adjusted R Square 0.9804
Standard Error 0.937
Observations 35
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ANOVA
df SS MS F Significance F
Regression 1 1572.55 1572.55 1791.30 0.000
Residual 34 28.97 0.88
Coefficient Standard Error t value P-value
Intercept 14.0842 3.4029 4.14 0.0002
Height 1.9754 0.0467 42.32 0.0000
1) How much variation is in the response variable is explained by the regression?

2) Is there evidence that height is a significant predictor of distance? Use α = 0.1
a) No, since p-value > 0.1
b) No, since p-value = 1791.3019
c) Yes, since p-value [removed] 0.1
e) No, since p-value [removed] 0.66
c) p  0.66
d) p = 0.66

18) What is the absolute value of the test statistic used to test this hypothesis?
a) 0.7139
b) 1.2522
c) 12.3978
d) 7.0678
e) 1.4392 I believe it is 1.635?
Test Statistic = (0.680 – 0.66 ) / sqrt( 0.66 ( 0.34 )/1500 ) =
19) Is there a significant difference between the mean quality ratings of each supplier using alpha equal 10%?
a) No, since t=1.7959; do not reject Ho
b) No, since t=1.2816; do not reject Ho
c) No, since Z=1.3634; do not reject Ho
d) Yes, since t=1.7959; reject Ho
e) Yes, since Z=1.3634; reject Ho
The next 2 questions refer to the following scenario: According to the Consumer Aerosol Products Council, when 100 adults were asked if it is true or false that aerosol cans may use CFC propellants (which eats the earth’s ozone), 40 adults knew that it was true. CFCs were banned in almost all sprays 20 years ago. Let p denote the true proportion of adults who knew that aerosol cans may use CFC propellants.
Sample
Those knowing that aerosol cans may use CFC propellants 40
Those not knowing that aerosol cans may use CFC propellants 60
20) Determine a 90% confidence interval for p.
a) 0.4
b) (0.2738, 0.5262)
c) (0.304, 0.496)
d) (-1.3271, 2.1271)
e) (0.3194, 0.4806)
21) What is the estimate of p?

The next 3 questions refer to the following situation. The caffeine content of a random sample of 34 of black coffee dispensed by a new machine is measured. The mean and standard deviation are 90.8 mg and 53.77 mg, respectively.
22) Calculate a 95% confidence interval for the true mean caffeine content per cup dispensed by the machine
a) (87.58, 94.02)
b) (72.04, 109.56)
c) (72.04, 94.02)
d) (88.95, 109.56)
e) (88.95, 92.65)

23) What margin of error was used in creating the confidence interval above?
a) 18.76
b) 173.01
c) 1.85
d) 351.98
e) 3.22
24) What is the sample size needed to obtain a margin of error of 10.97 with a 90% confidence interval?
n=34, xbar=90.8, s=53.77, E=10.97
a=0.1, |Z(0.05)|=1.645 (check standard normal table)
So n=(Z*s/E)^2
=(1.645*53.77/10.97)^2
=65.01276
Take n=66

The next 7 questions refer to the following scenario. A car manufacturer is interested in testing the stopping distance (in feet) of a vehicle with a certain type of tire. A sample of identical vehicles is chosen, and tire load (weight of the vehicle plus cargo) and speed are varied. Use tire load (X1) and vehicle speed (X2) to predict the stopping distance (Y).
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Regression Statistics
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R Square 0.9963
Adjusted R Square 0.996
Standard Error 0.939
Observations 52
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ANOVA
df SS MS F Significance F
Regression 2 11739.45 5869.73 6656.584 0
Residual 49 44.09 0.9
Total 51 11783.54
Coefficient Standard Error t value P-value
Intercept 67.3510 79.7801 0.84 0.4027
Load 0.0534 0.0200 2.67 0.0102
Speed 1.9739 0.0175 112.77 0.0000

25) How much variation in the variable distance is explained by the regression?

26) What is the estimated regression line?
a) distance = 67.351
b) distance = distance + 0.0534(Load) + 1.9739 (Speed)
c) distance = 67.3510 + 0.0534(Load) + 1.9739(Speed)
d) distance = (Intercept)(Load)(Speed)
e) distance = (Load)(Speed)
27) Use the estimated regression equation to predict the distance when, Load = 4010.78, Speed = 26.35.

28) Suppose one of the observations is: distance = 347.6, Load = 4015.75, Speed = 52.28. What is the residual?

29) What is the estimate of the standard error?

30) Which of the variables are dependent?
a) Load
b) Speed Load
c) Regression Residual Total
d) Intercept
e) Distance
31) What can be said about the relationship between distance and the predictors?
a) The relationship is median and IQR
b) There is not a significant relationship
c) Intercept is the best predictor of Load
d) There is a significant relationship
e) There is clearly a non-linear discrete relationship