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Utts - Seeing Through Statistics 4/e (Homework)

James Finch

Statistics, section 2, Fall 2019

Instructor: Dr. Friendly

Current Score : 14 / 101

Due : Sunday, January 27, 2030 23:30 EST

Last Saved : n/a Saving...  ()

Question
Points
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
3/3 1/20 5/7 0/2 1/6 1/3 3/3 –/1 0/2 –/8 –/5 –/3 –/7 –/4 –/9 –/18
Total
14/101 (13.9%)
  • Instructions

    Seeing through Statistics, 4th edition, by Jessica Utts and published by Cengage Learning, develops statistical literacy and critical thinking through real-world applications, with an emphasis on ideas, not calculations. This text focuses on the key concepts that educated citizens need to know about statistics. These ideas are introduced in interesting applied and real contexts, without using an abundance of technicalities and calculations that only serve to confuse students.

    New for Spring 2021! Question 1 is an example of a Concept Video Question. (CV) Concept Video questions provide students with a Concept Video along with two to three comprehension questions. Concept Videos are 7-10 minutes in length and are designed to help students with big picture understanding of statistics.

    New for Spring 2021! Question 2 is an example of a new Select Your Scenario question type. (SYS) Select Your Scenario problems provide students with 3 different contexts to choose from. They select the scenario most relevant to them, and then solve the problem. Regardless of which scenario the student chooses, they will be required to answer questions demonstrating knowledge of a learning objective, making them the perfect questions to assign toward the end of a chapter. Students can use SALT to answer this question.

    Question 3 showcases the ability to grade student responses using fill-in-the-blank sentences and multiple choice. Grading the answers this way avoids essay mode while still requiring the student to demonstrate that the key points are understood.

    Question 4 requires the student to select all correct answers simultaneously.

    Question 5 is an example of how boxplots are graded. Students can use SALT to answer this question.

    Question 6 includes an example of how histogram plots are graded. Students can use SALT to answer this question.

    Question 7 highlights the ability to grade numerical entries. Areas under normal curves are also shown featured. Students can use SALT to answer this question.

    Question 8 highlights pie charts and bar charts.

    Question 9 highlights time series plots and asks the student to identify which plot has misleading units.

    Question 10 highlights scatter plots and is typical of questions on regression found in this book. Students can use SALT to answer this question.

    Question 11 highlights the conceptual, rather than the computational, aspects of hypothesis testing and is typical of many of the questions found in this book.

    Question 12 is a Concept Question where students are asked to provide a short answer to a prompt, then answer a multiple choice question about the sample prompt, then reflect on their original answer.

    Question 13 is a Simulation Question utilizing the JMP Applet.

    Question 14 is a Stats in Practice Question that demonstrates the use of videos displayed within a question, followed by multiple-choice and discussion questions in a unique two-part accordion-style type of display.

    Question 15 is an example of a Statistical Lab.

    Question 16 highlights Milestone 1, the first step in presenting and tracking Project Milestones for a statistical research project. This demo assignment allows many submissions and allows you to try another version of the same question for practice wherever the problem has randomized values.

    The answer key and solutions will display after the first submission for demonstration purposes. Instructors can configure these to display after the due date or after a specified number of submissions.

Assignment Submission

For this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes if you submit or change the answer.

Assignment Scoring

Your last submission is used for your score.

1. 3/3 points  |  Previous Answers USeeStat4 1.CE.001.CV. My Notes
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1 2 3
1/1 1/1 1/1
3/100 1/100 1/100
Total
3/3
 
Watch the video below then answer the questions that follow.
  1. What is the first step in the statistical research process?
         Correct: Your answer is correct.
  2. It is important to have very strong math skills in order to be successful in a statistics course.
         Correct: Your answer is correct.
  3. Statistics is used in which of the following industries?
         Correct: Your answer is correct.
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2. 1/20 points  |  Previous Answers USeeStat4 8.SYS.002.S. My Notes
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1/1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1 /1
1/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100
Total
1/20
 
Select Your Scenario:
This problem contains data for 3 different scenarios: Travel and Tourism, Business, and Sports.
Read the scenarios, and once finished, you will be asked to select which scenario you would like to be assessed on.
You will not be asked to answer questions for the other 2 scenarios.
When you travel by airplane, have you ever wondered about whether your flight might be delayed from taking off or from landing? This is an important consideration as you will need to arrange transportation to your final destination after you arrive at the airport. To help track airline performance, the U.S. Bureau of Transportation Statistics of the Department of Transportation publishes statistics. For the purposes of this dataset, a flight is considered delayed if it arrived at (or departed from) the gate 15 minutes or more after the scheduled arrival (or departure) time as reflected in the Computerized Reservation System.
We will explore the distribution of monthly percentage of domestic flights delayed in the United States using a sample of data for the years 2010 through 2019 by making a histogram with bins starting at 9% and a bin width of 3%. We will then determine the z-scores for a delayed percentage of (a) 16% and (b) 25%.
The dataset consists of the percentage of flights delayed for each month for years 2010 through 2019 for domestic flights in the United States.
Airline Performance: Bureau of Transportation Statistics. (2020, September 1). On-Time Performance - Flight Delays at a Glance. United States Department of Transportation. https://www.transtats.bts.gov/HomeDrillChart.asp
Year Month Delayed (%)
2010 January 18.58
2010 February 19.66
2010 March 18.3
2010 April 13.83
2010 May 18.55
Undergraduate business students at a public university in the midwestern United States ran a café one semester and collected data each business day to help make sound business decisions and to be more profitable. Among other things, the daily total cash register sales were recorded.
We will explore the distribution of daily total sales for this café using a sample of data from one semester by making a histogram of Sales ($) with bins starting at $60 and a bin width of $25. We will then determine the z-scores for a day when total sales were (a) $200 and (b) $90.
The dataset consists of data recorded across one semester including an index number that puts the observations in chronological order, the day of the week, and the total sales in dollars.
http://jse.amstat.org/jse_data_archive.htm
Index Day of Week Sales($)
1 Tuesday 199.95
2 Wednesday 195.74
3 Thursday 102.68
4 Friday 162.88
5 Monday 101.76
It goes without saying that professional basketball players are tall. Height obviously matters when it comes to playing basketball and tall people are more efficient because they can reach the basket easily, allowing for more points per game, as well as more rebounds and blocked shots. If you watch National Basketball Association (NBA) games regularly, you certainly notice that many players are quite tall.
We will explore the distribution of NBA player heights using a sample of players active in the 2019-2020 season by making a histogram of "HEIGHT (INCHES)" with bins stating at 68 inches and a bin width of 2 inches. We will then determine the z-scores for players who are (a) 72 inches (6'0") and (b) 85 inches (7'1").
The dataset consists of the NBA player's name, team, and height, measured in inches, for players active in the 2019-2020 season.
https://www.nba.com/stats/players/bio/
Player Team Height (Inches)
Aaron Gordon ORL 80
Aaron Holiday IND 73
Abdel Nader OKC 77
Adam Mokoka CHI 77
Admiral Schofield WAS 77
Click the link below to begin the question by choosing a topic.
Pick your topic.
Choose the topic on which you would like to be assessed. Once you select your scenario, you cannot change your topic.
     Correct: Your answer is correct.
Note: If you select Skip, you will be assessed on the Travel and Tourism topic.
Question
Select Your Scenario:
First, select the tab that corresponds to the topic you chose above.
Note: Click the SALT button in the tab corresponding to the topic you chose.
When you travel by airplane, have you ever wondered about whether your flight might be delayed from taking off or from landing? This is an important consideration as you will need to arrange transportation to your final destination after you arrive at the airport. To help track airline performance, the U.S. Bureau of Transportation Statistics of the Department of Transportation publishes statistics. For the purposes of this dataset, a flight is considered delayed if it arrived at (or departed from) the gate 15 minutes or more after the scheduled arrival (or departure) time as reflected in the Computerized Reservation System.
We will explore the distribution of monthly percentage of domestic flights delayed in the United States using a sample of data for the years 2010 through 2019 by making a histogram with bins starting at 9% and a bin width of 3%. We will then determine the z-scores for a delayed percentage of (a) 16% and (b) 25%.
The dataset consists of the percentage of flights delayed for each month for years 2010 through 2019 for domestic flights in the United States.
Airline Performance: Bureau of Transportation Statistics. (2020, September 1). On-Time Performance - Flight Delays at a Glance. United States Department of Transportation. https://www.transtats.bts.gov/HomeDrillChart.asp
Year Month Delayed (%)
2010 January 18.58
2010 February 19.66
2010 March 18.3
2010 April 13.83
2010 May 18.55
Import the dataset into SALT for analyzing.
A button hyperlink to the SALT program that reads: Use SALT.
Undergraduate business students at a public university in the midwestern United States ran a café one semester and collected data each business day to help make sound business decisions and to be more profitable. Among other things, the daily total cash register sales were recorded.
We will explore the distribution of daily total sales for this café using a sample of data from one semester by making a histogram of Sales ($) with bins starting at $60 and a bin width of $25. We will then determine the z-scores for a day when total sales were (a) $200 and (b) $90.
The dataset consists of data recorded across one semester including an index number that puts the observations in chronological order, the day of the week, and the total sales in dollars.
http://jse.amstat.org/jse_data_archive.htm
Index Day of Week Sales($)
1 Tuesday 199.95
2 Wednesday 195.74
3 Thursday 102.68
4 Friday 162.88
5 Monday 101.76
Import the dataset into SALT for analyzing.
A button hyperlink to the SALT program that reads: Use SALT.
It goes without saying that professional basketball players are tall. Height obviously matters when it comes to playing basketball and tall people are more efficient because they can reach the basket easily, allowing for more points per game, as well as more rebounds and blocked shots. If you watch National Basketball Association (NBA) games regularly, you certainly notice that many players are quite tall.
We will explore the distribution of NBA player heights using a sample of players active in the 2019-2020 season by making a histogram of "HEIGHT (INCHES)" with bins stating at 68 inches and a bin width of 2 inches. We will then determine the z-scores for players who are 72 inches (6'0") and (b) 85 inches (7'1").
The dataset consists of the NBA player's name, team, and height, measured in inches, for players active in the 2019-2020 season.
https://www.nba.com/stats/players/bio/
Player Team Height (Inches)
Aaron Gordon ORL 80
Aaron Holiday IND 73
Abdel Nader OKC 77
Adam Mokoka CHI 77
Admiral Schofield WAS 77
Import the dataset into SALT for analyzing.
A button hyperlink to the SALT program that reads: Use SALT.
After you have clicked the tab for your selected topic and read the problem, answer the questions below.
(a)
Use SALT to summarize the data and fill in the following table, rounding values to four decimal places as needed.
Variable N Mean Standard Deviation Median Minimum Value Maximum Value
Numerical Variable (No Response) seenKey

529

(No Response) seenKey

78.3932

(No Response) seenKey

3.4505

(No Response) seenKey

78

(No Response) seenKey

69

(No Response) seenKey

89

(b)
Create a histogram with "Starting Point" and "Bin/Class Width" values asked for.
The distribution for this variable (No Response) seenKey

is

mound shaped and (No Response) seenKey

is

at least roughly symmetric.
(c)
Determine the relative standing for the two data values of interest using the z-score formula appropriate for samples. Round your answers to two decimal places.
Data value (a).
z = 
x x
s
 
 = (No Response) seenKey

-1.85

Data value (b).
z = 
x x
s
 
 = (No Response) seenKey

1.91

Data value (a) is (No Response) seenKey

1.85

standard deviations (No Response) seenKey

below

the mean whereas data value (b) is (No Response) seenKey

1.91

standard deviations (No Response) seenKey

above

the mean. (Remember to take the absolute value of the z-score to determine the number of standard deviations each data value is away from the mean.)
(d)
Most data points are within three standard deviations of the mean. In other words, most observations will have a z-score that is larger than 3 and less than 3.
Find the data value with a z-score of 3, rounded to two decimal places.
x = z · s + x
 = (No Response) seenKey

68.04

Find the data value with a z-score of 3, rounded to two decimal places.
x = z · s + x
 = (No Response) seenKey

88.74

Our sample's minimum value (No Response) seenKey

is not

further than 3 standard deviations below the mean. Our sample's maximum (No Response) seenKey

is

further than 3 standard deviations above the mean. Upon further inspection of the histogram in SALT it can be observed that (No Response) seenKey

almost all

observations would have a z-score between 3 and 3.
You have now completed the question.
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5/7
 
A study reported in the May 17, 2012, issue of The New England Journal of Medicine followed people for an average of 13 years and found that people who consumed two or more cups of coffee a day were less likely to die during the course of the study than those who drank no coffee.
(a)
Was this study a randomized experiment or an observational study? Explain how you know.
It was Correct: Your answer is correct. seenKey

an observational study

because coffee drinking over many years Incorrect: Your answer is incorrect. seenKey

cannot

be randomly assigned.
(b)
Based on this study, can it be concluded that drinking coffee causes people to live longer?
     Correct: Your answer is correct.
(c)
The following headlines appeared on news websites reporting these results. In each case, explain whether or not the conclusion in the headline is justified.
(i)
"Coffee positively associated with life expectancy"Source: http://www.coffeeandhealth. org/2012/05/21/coffee-positively-associated-with-life-expectancy/
Headline (i) Correct: Your answer is correct. seenKey

is

justified because it Correct: Your answer is correct. seenKey

does not

imply a causal relationship.
(ii)
"NIH Study: Coffee Really Does Make You Live Longer, After All"Source: http://www.theatlantic.com/health/archive/2012/05/nih-study-coffee-really-does-make-you-live-longer-afterall/ 257302/
Headline (ii) Correct: Your answer is correct. seenKey

is not

justified because it Incorrect: Your answer is incorrect. seenKey

does

imply a causal relationship.


Solution or Explanation
(a)
It was an observational study. Coffee drinking over many years cannot be randomly assigned.
(b)
No. A cause and effect conclusion cannot be made based on an observational study. There are likely to be other differences between those who drink coffee and those who do not, and perhaps those other differences have an effect on how long someone lives.
(c)
Headline (i) is justified because it does not imply a causal relationship. Headline (ii) is not justified because it does imply a causal relationship.
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0/1 0/1
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0/2
 
Suppose the administration at your school wants to know how students feel about a policy banning smoking on campus. Because they can't ask all students, they must rely on a sample.
(a)
Give an example of a sample they could choose that would not be representative of all students. (Select all that apply.)

(b)
Explain how you think they could get a representative sample. (Select all that apply.)
Incorrect: Your answer is incorrect.

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/1 /1 /1 /1 /1 1/1
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1/6
 
Consider the following list of ages.
59, 74, 54, 74, 55, 80, 63, 77, 73, 55, 91, 99, 82, 71, 93, 95, 75, 78, 70, 74, 79, 83, 76, 94, 93, 63, 34, 98, 63, 82, 79
A button hyperlink to the SALT program that reads: Use SALT.
(a)
Create a five-number summary for these ages.
Lowest Value Lowest quartile Median Highest quartile Highest value
(b)
Create a boxplot using the five-number summary from part (a).

Correct: Your answer is correct.

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1/3
 
Suppose the scores on a recent exam in your statistics class were as follows.
76, 95, 60, 94, 55, 85, 75, 94, 64, 85, 80, 90, 65, 75, 78, 33, 75, 65, 97, 74, 87, 63, 84, 67, 78, 76, 80, 85.
A button hyperlink to the SALT program that reads: Use SALT.
(a)
Create a histogram for the test scores.

Correct: Your answer is correct.
(b)
Explain how you decided how many intervals to use for the histogram in part (a).
    
(c)
Comment on the shape of the histogram in part (a).
    

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3/3
 
The 84th percentile for the Stanford-Binet IQ test is 115. (Recall that the mean is 100 and the standard deviation is 15.)
A button hyperlink to the SALT program that reads: Use SALT.
(a)
Verify that this is true by computing the standardized score and using Table 8.1 or SALT.
z = Correct: Your answer is correct. seenKey

1

(b)
Draw pictures of the original and standardized scores to illustrate this situation, similar to the pictures in Figure 8.4.
original scores

Correct: Your answer is correct.
standardized scores

Correct: Your answer is correct.


Solution or Explanation
(a)
The standardized score is
(115 100)
15
 = 1.00;
by Table 8.1 this is the 84th percentile.
(b)
Both pictures are identical bell-shaped curves. The top picture should be centered at 100 and have a line at 115, with 84% of the area below the line at 115 and 16% of the area above it. The bottom picture should look identical, except it is centered at 0 and has the line at 1 instead of 115.
A bell shaped curve is drawn on the graph labeled "IQ Scores". The curve enters the window just above the horizontal axis, goes up and right, changes direction at approximately 100 on the horizontal axis, goes down and right, and exits the window just above the horizontal axis. The area under the curve to the left of 115 is shaded.
A bell shaped curve is drawn on the graph labeled "Standardized Scores". The curve enters the window just above the horizontal axis, goes up and right, changes direction at approximately 0 on the horizontal axis, goes down and right, and exits the window just above the horizontal axis. The area under the curve to the left of 1 is shaded.
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/1
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/1
 
Use the pie charts below, create a bar graph comparing eye colors for males and females.
A pie chart titled "Males" has 4 slices of different sizes. The labels and approximate size of the slices are as follows.
  • Blue: 36.9%.
  • Brown: 34.2%.
  • Green: 13.7%.
  • Hazel: 15.2%.
A pie chart titled "Females" has 4 slices of different sizes. The labels and approximate size of the slices are as follows.
  • Blue: 30.0%.
  • Brown: 35.3%.
  • Green: 18.1%.
  • Hazel: 16.6%.

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0/2
 
Figure 9.12a, which displays rising postal rates, is an example of a graph with misleading units because the prices are not adjusted for inflation. The graph actually has another problem as well. Use the checklist in Section 9.6 to determine the problem; then redraw the graph correctly (but still use the unadjusted prices).

Incorrect: Your answer is incorrect.
Comment on the difference between Figure 9.12a and your new picture.
     Incorrect: Your answer is incorrect.


Solution or Explanation
The problem is that the years on the horizontal axis are not evenly spaced. They reflect when prices changed. If redrawn correctly the increases over the years are less even. To be truly accurate, there should be immediate jumps at the times the prices changed, rather than showing gradual change. See the figure below.
The graph contains a series of 10 points connected by line segments. The horizontal axis has values from 71 to 95. All of the points occur at labeled tickmarks that are unevenly spaced along the horizontal axis.
  • The segments start at (71, 8),
  • go right to (74, 8),
  • go up to (74, 10),
  • go right to (75, 10),
  • go up to (75, 13),
  • go right to (78, 13),
  • go up to (78, 15),
  • go right to (3/81, 15),
  • go up to (3/81, 18),
  • go right to (11/81, 18),
  • go up to (11/81, 20),
  • go right to (85, 20),
  • go up to (85, 22),
  • go right to (88, 22),
  • go up to (88, 25),
  • go right to (91, 25),
  • go up to (91, 29),
  • go right to (95, 29),
  • and go up to stop at (95, 32).
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/8
 
The table below gives the self-reported heights of 10 college women ("daughter's height"), along with the heights of their mothers.
Daughter's height (y) Mother's height (x)
60 62
68 67
65 64
66 65
67 65
62 63
69 65
63 61
61 59
65 67
A button hyperlink to the SALT program that reads: Use SALT.
(a)
Draw a scatter plot for these data, placing Mother's height (in inches) on the horizontal axis and Daughter's height (in inches) on the vertical axis.

Comment on whether or not it looks like there is a general linear relationship and, if so, whether it is positive or negative.
    
(b)
Using Excel, SALT, a calculator, or other software, find the correlation between the mother's and daughter's heights (in inches). (Round your answer to four decimal places.)
Do the value and the sign (positive or negative) make sense based on the scatterplot from part (a)? Explain.
It makes sense because the scatter plot shows relationship.
(c)
Using Excel, SALT a calculator, or other software, find the intercept and slope for the regression equation with
x = mother's height (in inches)
and
y = daughter's height (in inches).
(Round your answers to four decimal places.)
intercept slope
(d)
The equation you found in part (c) might be useful for predicting the height (in inches) of a female from her mother's height (in inches) before the daughter is fully grown. Use the equation to predict the height (in inches) of the daughter of a mother who is 62 inches tall. (Round your answer to one decimal place.)
in

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/5
 
The news story discussed in Case Study 6.5 (pp. 132-133) was headlined "NIH study finds that coffee drinkers have lower risk of death"(Source: http://www.nih.gov). The news story was based on an article published in The New England Journal of Medicine(Freedman et. al., 2012) that followed hundreds of thousands of older adults from 1995 to 2008 and examined the association between drinking coffee and longevity.
(a)
What are the null and alternative hypotheses for this study?
null hypothesis
    
alternative hypothesis
    
(b)
The authors concluded that those who drank coffee had a statistically significantly lower risk of death (during the time period of the study) than those who did not. Which type of error, type 1 or type 2, could have been made in making this conclusion?
    
(c)
Explain what a type 1 error would be in this situation.
    
Explain what a type 2 error would be in this situation.
    
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/3
 
Concept Question
This question is related to sampling distribution.
Part 1 of 3
If a normal population has a standard deviation σ = 38.9, what is the standard error of the mean (standard deviation of the x's) if samples of size 16 are selected? What is the standard error if samples of size 49 are taken? What is the standard error if samples of size 100 are taken? (Round your answers to two decimal places.)
Regardless of sample size, why is the standard deviation of the x's always smaller than the standard deviation of the population?

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/7
 
Waiters at a restaurant want to know if there is a relationship between the amount they are given in tips and the amount of the meal. Here is the graph along with the output from the regression table (without the regression equation). Use the JMP applet to answer the questions below.
  • JMP Applet

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Stats in Practice

  • Part I - Multiple Choice Questions

    The video opens with: "Fewer young people are putting on sunscreen when they are having fun in the sun." They support this conclusion by citing the results of a Center for Disease (CDC) study, in which researchers estimated what value in both 2001 and 2011?
        
    In this CDC study, why is it correct to say that researchers "estimated" a particular population characteristic rather than say the researchers "calculated" that value?
        
    The video discusses a study conducted by University of Michigan researchers who found that "close community ties can reduce heart attack risk for those over 50." In this study, researchers probably collected a sample of individuals, and for each, measured numerical variables (such as age or weight) as well as categorical variables (such as gender or whether a person has had a heart attack). Which of the following is also a numerical variable that researchers may have measured in this study?
        
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15. /9 points USeeStat4 9.Lab.001.Excel. My Notes
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/9
 

Statistical Lab

  • Background

    The National Institutes of Health conducts ongoing surveys of US adults called the Health Information National Trends Survey (hereafter abbreviated HINTS).
    From the National Institutes of Health: "The HINTS data collection program was created to monitor changes in the rapidly evolving field of health communication. Survey researchers are using the data to understand how adults 18 years and older use different communication channels, including the Internet, to obtain vital health information for themselves and their loved ones...."
    A doctor and a patient are talking in an examination room.
    The most recent round of data collection occurred over the course of September 2013November, 2013 in HINTS 4 Cycle 3. In this lab, you will be using a subset of the HINTS 4 Cycle 3 data to practice creating effective and informative graphical representations of data, which may include histograms and pie charts.
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16. /18 points USeeStat4 PJT.1.001. My Notes
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/18
 

Milestone 1: Research Design

  • Question 1

    What is your research question?
    Your research question should be based on a topic that interests you and that you can reasonably obtain data for. Try to make your research question as specific as possible. Form a research question about a population that you will be able to sample. Some examples of research questions are: "Are students at my college able to taste the difference between regular coffee and decaffeinated coffee?", "Does the GPA, age, and number of credits needed for graduation for juniors at my university differ between transfer students and non-transfer students?", "Have the new water rates in my water district changed residents' water usage habits?", and "Do recent graduates from the business department at my university get larger starting salaries on average if they have participated in a summer internship?"

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