Part A -
Question 1: Which of the plots has the strongest linear association?
A) Plot 1
B) Plat 2
C) Plot 3
D) Plot 4
Question 2: Which of the plots has the strongest nonlinear association?
A) Plot 1
B) Plot 2
C) Plot 3
D) Plot 4
Question 3: Which of the plots has negative linear association?
A) Plot 1
B) Plot 2
C) Plot 3
D) Plot 4
Question 4: The four correlation coefficients for the scatterplots shown are -0.1169, 0.7699, -0.9396, and 0.1632.
Which one of these correlation coefficient values is the most appropriate choice for the data shown in Plot 1?
A) -0.1169
B) 0.7699
C) -0.9396
D) 0.1632
Question 5: Note that the automobile fuel efficiency is often measured in miles that the car can be driven per gallon of fuel (mpg).
Which of the following graphs shows that heavier cars tend to have lower fuel efficiencies?
A) Plot A
B) Plot B
C) Plot C
Question 6: For the following problem, suppose we have a collection of cars, we measure their weights and fuel efficiencies and generate the following graph of the data.
Tell whether the following statement is valid or invalid.
The strong association proves that more weight causes a lower mpg rating.
A) Valid
B) Invalid
Question 7: In a study of 6-11 year old elementary school children, data shows a strong positive correlation between measures of physical coordination and math scores. For example, scores on arithmetic problems are strongly associated with the time it take to run a 50-yard race, r = 0.83.
What can we conclude?
A) Arithmetic improves coordination,
B) To improve arithmetic scores the school should require students to get exercise, like running
C) Age is a probably lurking variable in this study.
Part B -
Question 1: Automobile fuel efficiency is often measured in miles that the car can be driven per gallon of fuel (mpg), Heavier cars tend to have lower fuel efficiencies (rower mpg ratings). Which variable (weight or fuel efficiency) is most naturally considered the explanatory (predictor) variable in this context?
A) Weight
B) Fuel efficiency
Question 2: Suppose that we have the least squares regression line Y = 3 + 2X and that the sum of the squares of the errors (SSE) for this line is 13,712. What can be said about the sum of the squares of the errors (SSE) for this data set and the line Y = 3 + 2.5X?
A) The sum of the squares of the errors (SSE) for ate line Y = 3 + 2.5X will be 13,712.
B) The sum of the squares of the errors (SSE) for the line Y = 3 + 2.5X will be greater than 13,712.
C) The sum of the squares of the errors (SSE) for the line Y = 3 + 2.5X will be less than 13,712.
D) It is impossible to tell how the sum of the squares of the errors (SSE) for the line Y = 3 + 2.5X will relate to 13,712.
Question 3: The slope of the least squares regression line is given by
r(sy/sx)
where r is the correlation coefficient, sx is the standard deviation of the X-values, and sy is the standard deviation of the Y-values. If r = 0.75, sx = 3 and sy = 2, then how much should we expect Y to increase for every one unit of increase in X?
A) 0.5 units
B) 1.125 units
C) 0.75 units
D) 0.67 units
Question 4: Note that automobile fuel efficiency is often measured in miles that the car can be driven per gallon of fuel {mpg). Suppose we have a collection of cars, we measure their weights and fuel efficiencies, and generate the following graph of the data.
Which of the following can possibly be the regression line for this data set.
A) Y = - 1.11X + 5.17
B) Y = 1.11X + 68.17
C) Y = -1.11 X + 68.17
D) Y = -1.11X2 + 68.17
Question 5: Suppose that we have found that the least squares regression line for this data set is Y = -1.11X + 68.17, where X represents the weight of the cars in hundreds of pounds and Y represents the mpg rating.
Notice that the regression line for this data set has slope -1.11. Which of the following statements is the most complete, valid conclusion about the relationship between weight and fuel efficiency?
A) Heavier cars tend to have lower mpg ratings.
B) For every 100 pound increase in car weight we expect to see a 1.11 mpg increase in fuel efficiency.
C) For every 100 pound increase in car weight we expect to see a 1.11 mpg decrease in fuel efficiency.
D) For every 1 pound increase in car weight we expect to see 1.11 mpg decrease in fuel efficiency.
Question 6: Suppose that we have found that the least squares regression line for this data set is Y = -1.11X + 68.17, where X represents the weight of the cars in hundreds of pounds and Y represents the mpg rating.
Notice that Y -intercept of the least squares regression line is 68.17. Provide an interpretation of this Y-intercept and tell whether such an interpretation is appropriate in this situation.
A) We expect that a car that weighs 0 lbs would have a fuel efficiency rating of 68.17 mpg. This is an appropriate interpretation in this context.
B) We expect that a car that weighs 0 lbs would have a fuel efficiency rating 68.17 mpg. This is not an appropriate interpretation in this context because of extrapolation.
C) For every 100 pound increase in weight we expect to see a 68.17% increase in mpg rating.
Question 7: Suppose that we have found that the least squares regression line for this data set is Y = -1.11X + 68.17, where X represents the weight of the cars in hundreds of pounds and Y represents the mpg rating.
Use the given equation of the regression line given to predict the mpg rating of a car that weight 3700 lbs.
A) 27.1 mpg
B) 64.063 mpg
C) 4038.83 mpg
D) -4038.83 mpg
Question 8: Suppose that we have found that the least squares regression line for this data set is Y = -1.11X + 68.17, where X represents the weight of the cars in hundreds of pounds and Y represents the mpg rating.
Notice that this regression model predicts that a car weighing 4200 pounds has a mpg rating of 21.55 mpg. Would it be appropriate to use this model to predict the fuel efficiency rating of a car weighing 7000 pounds? Why or why not?
A) Yes. Wt can just plug in X = 70 into the equation and compute the predicted mpg rating.
B) No. The heaviest car in the data set weighs approximately 5500 pounds (and the second heaviest weighs around 4500 pounds). This would be extrapolating too far out From the data set.
Part C -
Question 1. A researcher conducted a study to determine if aspirin reduces the chance of a heart attack. He randomly assigned 250 patients to take aspirin every day and 250 patients to take a placebo every day. After a certain length of time he reported the percentage of heart attack s for each group. Is this an observational or an experimental study and why?
a) The study is observational because it involves random assignment of treatments to patients.
b) The study is observational because it involves observing who had heart attacks.
c) The study is experimental because it involves random assignment of treatments to patients.
d) The study is experimental because it involves observing who had heart attacks.
Question 2. A health report provides the following information,
New research suggests that regular exercise may increase resistance to colds. In a recent study, 300 healthy volunteers were given nasal sprays that contained a cold virus. The volunteers were quarantined for five days. The volunteers were asked how many hours per week, on average, they spend exercising. The researchers found that volunteers who reported that they exercise less than one hour per week were four times as likely to get a cold as those who reported that they exercised, on average, five or more hours. The average number of hours spent exercising, per week, seems to have been the most significant factor for volunteers ability to resist getting the cold virus, That is, those who reported exercising more were also significantly more able to resist getting a cold.
The study results fail short. That is they don't completely demonstrate that increasing the amount of time we exercise will increase our resistance to catching a cold? Why not? (Choose the best answer).
a) The age and gender of the volunteers was not specified.
b) We are not told what day of the week they got the nasal spray.
c) The subjects could have lied about their exercising times.
d) The time of exercising was not randomly assigned.
Question 3. A recent macular degeneration study suggests that certain nutrient found in green leafy vegetables, can slow the onset and progress of this disease, In this study, a grow of older adults were divided into two groups.
People in Group A ate green leafy vegetables five or more times a week. People in Group B ate green leafy vegetables less than two times a week. Group B had a significantly higher rate of macular degeneration than Group A. Group B also had more severe oases of macular degeneration than the people in Group A. Which of the following is the sample for this study?
a) The group of older adults before they are divided into groups.
b) The group of older adults who ate green leafy vegetables 5 or more times a week.
c) The group of older adults who ate green leafy vegetables fewer than two times a week.
d) All older adults with macular degeneration.
Question 4. A student in a statistics class is trying to determine the most popular vehicle color for students at the college he attends. He conducted a survey of 80 students to gather his data and found that 20 students drove black cars, 17 students drove white cars, 15 students drove silver cars, 11 students drove tan cars, 9 students drove red cars and 8 students drove blue cars. Now he is trying to summarize this data graphically. He cannot decide whether he should a bar chart or a dot plot. Which graphing method should he use?
a) Bar chart
b) Dot plot
c) Either a bar chart or a dot plot
d) Neither a bar chart nor a dot plot
Question 5. Research conducted a study of treatments for angina (pain due to low blood supply to the heart) which compared the effectiveness of three different treatments: bypass surgery, angioplasty, and prescription medication only. The researchers looked at the medical records of thousands of patients with angina whose doctors had chosen one of these treatments. The researchers concluded that prescription medications only is the most effective treatment and should be used for all patients because patients who had received that treatment had the highest median survival time. Which statement best describes if the researchers conclusion is valid and why?
a) The conclusion is valid because the patients taking prescription medications lived longer.
b) The conclusion is valid because the study was a comparative experiment.
c) The conclusion is not valid because the doctors assigned the treatments.
d) The conclusion is not valid because the patients volunteered to be studied.
Question 6. A researcher conducted a study to determine if aspirin reduces the chance of a heart attack. He randomly assigned 250 patients to take aspirin every day and 250 patients to take a placebo every day. After a certain length of time he reported the percentage of heal attacks for the patients who took aspirin every day and for those who did not take aspirin every day. What is the treatment in the study described above?
a) The daily aspirin regimen.
b) The daily placebo regimen.
c) The occurrence of a heart attack.
d) The 250 patients randomly assigned to take aspirin every day.
Question 7. In the study described above, what is the most important reason for the researcher to randomly assign patients to one of the two groups?
a) So that the results of the study will generalize.
b) So that there is an equal number of people in both groups for the experiment.
c) So that there is no real difference between the two groups prior to the treatment.
d) So that equal amounts of aspirin and placebo would be used during the experiment.
Question 8. A researcher is studying fashion trends of college students on a particular campus. He decides to randomly select 200 students that attend the college and ask them to complete a survey to determine trends. Which of the following BEST describes the target population in this study?
a) Fashion trends
b) College-aged people
c) Students that attend the college
d) The 200 students that are asked to complete the survey
Question 9. We want to know the average (or typical] age of students attending our college. The registrar's office was able to give us the data for the entire student population. What is the most appropriate graphical display to summarize this data?
a) Pie Chart
b) Histogram
c) Bar Graph
d) Scatter Plot
Part D -
Question 1. Job satisfaction surveys have shown that a person's job satisfaction is often related to their academic major. The table below summarizes the results of a job satisfaction survey of college graduates who are currently working in a full-time job.
|
|
Frequency (Rel. Freq.)
|
|
College Major
|
Satisfied
|
Unsatisfied
|
|
Accounting
|
90 (43.1%)
|
35 (30.2%)
|
|
Linguistics
|
24 (11.5%)
|
36 (31%)
|
|
Engineering
|
95 (45.4%)
|
45 (38%)
|
|
Total
|
209 (100%)
|
116 (100%)
|
(a) Find the missing relative frequencies.
(b) Sketch the Bar-Charts of the relative frequencies for both groups.
Question 2. A researcher wants to understand if walking rates of males and females were different. She used a sample of 10 males and 10 females who walked the 2014 Seattle Half Marathon. The number of hours required by each person to complete the 13.1 mile walk is given below.
|
Males
|
1.9
|
2.7
|
2.9
|
2.9
|
3.4
|
3.4
|
3.7
|
4.0
|
4.0
|
4.4
|
|
Females
|
2.8
|
2.9
|
3.0
|
3.4
|
3.4
|
3.6
|
3.6
|
3.6
|
3.7
|
4.0
|
(a) Determine and enter the five-number summary for the walk times of the male and female participants.
(b) Calculate the interquartile Range (IQR) for each data set and identify any outliers.
(c) Compare the Meals and Females data sets by drawing the box-plot for each group.
(d) Describe the similarities and differences in performance among men and women in terms of shape, center and spread.
(e) Complete the table below and calculate the means for both and the standard deviation for the females participating in this study?
|
|
Males
|
Females
|
|
Deviation
|
Deviation Squared
|
|
|
X
|
Y
|
Y2
|
Y - Y-
|
(Y - Y-)2
|
|
1
|
1.9
|
2.8
|
7.84
|
|
0.36
|
|
2
|
2.7
|
2.9
|
8.41
|
-0.5
|
0.25
|
|
3
|
2.9
|
3.0
|
9.00
|
-0.4
|
0.16
|
|
4
|
2.9
|
3.4
|
|
0
|
0
|
|
5
|
3.4
|
3.4
|
11.56
|
|
0
|
|
6
|
3.4
|
3.4
|
12.96
|
0.2
|
|
|
7
|
3.7
|
3.6
|
12.96
|
0.2
|
0.04
|
|
8
|
4.0
|
3.6
|
|
0.2
|
0.04
|
|
9
|
4.0
|
3.7
|
13.69
|
|
0.09
|
|
10
|
4.4
|
4.0
|
16.00
|
0.6
|
036
|
|
∑
|
33.3
|
34.0
|
116.94
|
|
|
(f) What would you think are the better set of statistics to describe and compare the two groups. (1) the means and standard deviations or (2) the medians and inter-quartile ranges. Why? (Himont: Consider the shape of the distributions).
Question 3. The table below shows data collected from students at Los Medanos in 2009. The variable, credits, is the number of credits each students that semester. The variable, textbooks, is the amount students spent on the textbooks that were required for their courses that semester. The credits and textbooks data come from student reports on a survey.
|
Credits
|
3
|
4
|
9
|
12
|
14
|
16
|
8
|
1
|
6
|
15
|
9
|
4
|
12
|
12
|
12
|
|
Textbooks
|
120
|
66
|
465
|
430
|
397
|
475
|
208
|
50
|
49
|
685
|
220
|
172
|
302
|
460
|
530
|
(a) The explanatory variable (x) is:
(b) The response variable (y) is:
(c) The mean cost of the textbooks is $308.60. Calculate the mean number of credits.
(d) Create a scatterplot of the data set above and include the means for the variables.
(e) Describe the form, strength, and direction of the pattern.
(f) Give a reasonable estimate to the value of r, the correlation coefficient.
(g) Use the LSR line y^ = 36.97 x - 29.08 to predict the amount spent on textbooks for a students taking 12 units.
(h) Extra Credit: Add the LSR line to the graph with your scatterplot of the data. Verify that the point (x-, y-) is on your line.
Extra Credit Question:
A statistics instructor posted the following information on her office door at the end of the semester.
|
|
Mean
|
Standard Deviation
|
Correlation Coefficient
|
|
Midterm Score
|
72.8
|
6.2
|
.83
|
|
Final Score
|
78.5
|
8.8
|
(a) Find the slope and y-intercept for the LSR line.
(b) If Karen earned an 82 on the midterm what is a reasonable estimate to the grade she's likely to get on the final, (assuming she has maintained her good study habits)?
Attachment:- Assignment File.rar