WorksheetsChapter 12 Review
Total questions: 19
Worksheet time: 5hrs 45mins
Name
Class
Date
1.
Which one of the following provides evidence that a condition for regression inference has been met?
a)
A histogram of the values for the explanatory variable shows a roughly linear form.
b)
A scatterplot of the residuals against the values of the explanatory variable displays a random scattering of points about the line residuals = 0.
c)
The data consists of at least 30 observations.
2.
Is there a relationship between reaction time and age? A statistics student measures the reaction time of 12 subjects by measuring how far a yardstick drops, in inches, before a subject catches it between his or her thumb and forefinger (a high number thus indicates a slow reaction time). The student plans to use linear regression to see if reaction time can be predicted by the age of the subject. Which one of the following is a correct set of hypotheses for testing the significance of this relationship?
a)
H0: β = 1; Ha : β ≠ 1, where β = the true slope of the population regression line.
b)
H0 : β = 0; Ha : β ≠ 0 where β = the true slope of the population regression line.
c)
H0 : ρ = 1; Ha : ρ < 1 where ρ = the true population correlation between age and reaction time.
3.
Is there a relationship between reaction time and age? A statistics student measures the reaction time of 12 subjects by measuring how far a yardstick drops, in inches, before a subject catches it between his or her thumb and forefinger (a high number thus indicates a slow reaction time). The student plans to use linear regression to see if reaction time can be predicted by the age of the subject. Output from a computer regression analysis is given.
Which one of the following is a correct interpretation of the quantity S = 3.06911?
Which one of the following is a correct interpretation of the quantity S = 3.06911?
a)
The typical distance between observed reaction times and the mean reaction time is 3.06911 units.
b)
The typical distance between observed ages and the mean age is 3.06911 years.
c)
Predictions of reaction time from age based on this regression model will be off by an average of about 3.0691 units.
4.
Sarah runs an ice cream stand at a beach resort, and she is interested in predicting each day’s ice cream sales (in dollars) from the air temperature at 8:00 am (in degrees Fahrenheit). She randomly selects 12 days during the previous summer and calculates a least squares regression of sales on air temperature. A computer output of her regression is given.
Which one of the following is a correct interpretation of the number 1.646?
Which one of the following is a correct interpretation of the number 1.646?
a)
For each 1º increase in air temperature, ice cream sales are prediction to increase, on average, by $1.65.
b)
For samples of size 12, the typical deviation of a sample slope from the population (true) slope is estimated to be 1.646.
c)
For this sample, the typical distance between an observed temperature and the mean temperature is 1.646.
5.
With practice, people become faster at solving a certain type of mathematical puzzle. Fourteen college students were allowed to practice completing a certain type of mathematical puzzle for different amounts of time. Afterwards, each student's completion time on a new puzzle was measured. A scatterplot of the natural logarithm of Completion Time versus Practice Time showed a strongly linear relationship. Which of the following describes the relationship between completion time and practice time?
a)
Completion time is a power function of Practice Time.
b)
Completion time is an exponential function of Practice Time.
c)
Completion time is a logarithmic function of Practice Time.
6.
Is there a relationship between reaction time and age? A statistics student measures the reaction time of 12 subjects by measuring how far a yardstick drops, in inches, before a subject catches it between his or her thumb and forefinger (a high number thus indicates a slow reaction time). The student plans to use linear regression to see if reaction time can be predicted by the age of the subject. Output from a computer regression analysis is given.
The equation of the least-squares regression line is
The equation of the least-squares regression line is
a)
y-hat = 2.580 + 0.30809x
b)
y-hat = 2.580x + 0.30809
c)
y-hat = 2.716+ 0.05051x
7.
Is there a relationship between reaction time and age? A statistics student measures the reaction time of 12 subjects by measuring how far a yardstick drops, in inches, before a subject catches it between his or her thumb and forefinger (a high number thus indicates a slow reaction time). The student plans to use linear regression to see if reaction time can be predicted by the age of the subject. Output from a computer regression analysis is given.
Which of the following is the correct decision for the test of H0 : β = 0 versus Ha : β ≠ 0 at the a = .01 level? Assume all conditions for inference have been met.
Which of the following is the correct decision for the test of H0 : β = 0 versus Ha : β ≠ 0 at the a = .01 level? Assume all conditions for inference have been met.
a)
Because the P-value is less than a = .05, we reject . There is strong evidence of a linear relationship between age and reaction time.
b)
Because the P-value is less than a = .05, we fail to reject . We do not have evidence of a linear relationship between age and reaction time.
c)
Because the P-value is 0.365, which is more than a = .05, we fail to reject . We do not have evidence of a linear relationship between age and reaction time.
8.
Sarah runs an ice cream stand at a beach resort, and she is interested in predicting each day's ice cream sales (in dollars) from the air temperature at 8:00 am (in degrees Fahrenheit). She randomly selects 12 days during the previous summer and calculates a least squares regression of sales on air temperature. A computer output of her regression is given.
Which of the following is a correct expression for the 95% confidence interval for the slope of the population regression equation for the relationship between Air Temperature and Ice Cream sales?
Which of the following is a correct expression for the 95% confidence interval for the slope of the population regression equation for the relationship between Air Temperature and Ice Cream sales?
a)
16.063 ± 2.201 (1.646/√12)
b)
16.063 ± 2.228 (1.646)
c)
16.063 ± 2.201 (1.646)
d)
16.063 ± 2.228 (40.7502/√12)
9.
With practice, people become faster at solving a certain type of mathematical puzzle. Fourteen college students were allowed to practice completing a certain type of mathematical puzzle for different amounts of time. Afterwards, each student's completion time on a new puzzle was measured. The residual plot below is for a least-squares linear regression of y = time for completing the new puzzle versus x = the amount of practice time allowed.
a)
There is a no relationship between Practice Time and Puzzle Completion Time.
b)
This regression equation would likely overestimate the Puzzle Completion Time for 175 minutes of practice time.
c)
There is a non-linear relationship between Practice Time and Puzzle Completion Time.
10.
Forestry managers keep records giving the number of board feet B (in hundreds of board feet) of lumber produced by harvesting white pine trees with diameter D (in inches), so that they can predict the amount of lumber that can be harvested from a tree from its diameter. A scatterplot of B vs. D shows a strongly curved shape, but taking the natural logarithm of both variables produces a linear scatterplot. This computer output below is for a least squares linear regression of ln (B) vs ln (D) for 9 white pine trees.
Which one of the following is a correct regression equation for these data?
Which one of the following is a correct regression equation for these data?
a)
ln(B)-hat = -5.2484 + 3.0232*ln(D)
b)
ln(B)-hat = 3.0232 - 5.2484 * ln(D)
c)
ln(D)-hat = -5.2484 + 3.0232*ln(B)
d)
ln(B)-hat = -5.2484 + 3.0232*D
11.
With practice, people become faster at solving a certain type of mathematical puzzle. Fourteen college students were allowed to practice completing a certain type of mathematical puzzle for different amounts of time. Afterwards, each student's completion time on a new puzzle was measured. A scatterplot of the base 10 logarithm of Completion Time (in minutes) versus Practice Time (in minutes) showed a strongly linear relationship. A computer output of the least-squares regression of log10(Completion Time) versus Practice Time is given below.
Which one of the following is the predicted Completion Time for a student who practices for 150 minutes?
Which one of the following is the predicted Completion Time for a student who practices for 150 minutes?
a)
2.6 minutes
b)
8.7 minutes
c)
25.9 minutes
12.
Which of the following is not one of the conditions that must be satisfied in order to perform inference about the slope of a least-squares regression line?
a)
For each value of x, the population of y-values is Normally distributed.
b)
The standard deviation σ of the population of y-values corresponding to a particular value of x is always the same, regardless of the specific value of x.
c)
The sample size—that is, the number of paired observations (x, y)–exceeds 30.
d)
The data come from a random sample or a randomized experiment.
13.
Inference about the slope β of a least-squares regression line is based on which of the following distributions?
a)
The t distribution with n − 1 degrees of freedom
b)
The standard Normal distribution
c)
The Normal distribution with mean μ and standard deviation σ
d)
The t distribution with n − 2 degrees of freedom
14.
In golf, is that good putting is more important than long driving for shooting low scores? Data from a random sample of 69 of the nearly 1000 players on the PGA Tour’s world money list are examined. The average number of putts per hole and the player’s total winnings for the previous season are recorded. A least-squares regression line was fitted to the data.
The correlation between total winnings and average number of putts per hole for these players is
The correlation between total winnings and average number of putts per hole for these players is
a)
−0.285.
b)
−0.081.
c)
−0.007.
d)
0.081.
15.
Suppose that the researchers test the hypotheses H0: β = 0, Ha: β < 0. The value of the t statistic for this test is
a)
2.61.
b)
2.44.
c)
0.081.
d)
−2.44.
16.
The P-value for the test in the previous question is 0.0087. A correct interpretation of this result is that
a)
the probability that there is no linear relationship between average number of putts per hole and total winnings for these 69 players is 0.0087.
b)
if there is no linear relationship between average number of putts per hole and total winnings for the players in the sample, the probability of getting a random sample of 69 players that yields a least-squares regression line with a slope of —4139198 or less is 0.0087.
c)
if there is no linear relationship between average number of putts per hole and total winnings for the players on the PGA Tour’s world money list, the probability of getting a random sample of 69 players that yields a least-squares regression line with a slope of —4139198 or less is 0.0087.
d)
the probability of making a Type I error is 0.0087.
17.
A 95% confidence interval for the slope β of the population regression line is:
(the sample size was 69)
(the sample size was 69)
a)
7,897,179 ± 3,023,782.
b)
7,897,179 ± 6,047,564.
c)
−4,139,198 ± 3,328,807.
d)
−4,139,198 ± 3,396,742.
18.
Which of the following would provide evidence that a power law model of the form y = axb, where b ≠ 0 and b ≠ 1, describes the relationship between a response variable y and an explanatory variable x?
a)
A scatterplot of y versus x looks approximately linear.
b)
A scatterplot of ln y versus x looks approximately linear.
c)
A scatterplot of y versus ln x looks approximately linear.
d)
A scatterplot of ln y versus ln x looks approximately linear.
19.
It is easy to measure the circumference of a tree’s trunk, but not so easy to measure its height. Foresters developed a model for ponderosa pines that they use to predict tree’s height (in feet) from the circumference of its trunk (in inches):
ln(h-hat) = -1.2 + 1.4(lnC)
A lumberjack finds a tree with a circumference of 60 inches, how tall does this model estimate the tree to be?
ln(h-hat) = -1.2 + 1.4(lnC)
A lumberjack finds a tree with a circumference of 60 inches, how tall does this model estimate the tree to be?
a)
5ft
b)
11ft
c)
83ft
d)
93ft
100 %
