• Home
  • Textbooks
  • Statistics Learning From Data
  • An Overview of Statistical Inference—Learning from Data

Statistics Learning From Data

Thomas H. Short, Roxy Peck

Chapter 7

An Overview of Statistical Inference—Learning from Data - all with Video Answers

Educators

Section 1

Statistical Inference—What You Can Learn from Data

03:32

Problem 1

The report "Teens and Distracted Driving: Texting, Talking and Other Uses of the Cell Phone Behind the Wheel" (Pew Research Center, November 16,2009 ) summarizes data from a survey of a representative sample of 800 teens between the ages of 12 and 17 . The following statements were made on the basis of the resulting data:
$75 \%$ of all American teens own a cell phone. $66 \%$ of all American teens use a cell phone to send and receive text messages. $26 \%$ of American teens ages $16-17$ have used a cell phone to text while driving. Are the inferences made ones that involve estimation or ones that involve hypothesis testing? (Hint: See Example 7.1.)

Sheryl Ezze
Sheryl Ezze
Numerade Educator
View

Problem 2

For the study described in the previous exercise, answer the following questions.
a. What is the population of interest?
b. What population characteristics are being estimated?
c. Do you think that the actual percentage of all American teens who own a cell phone is exactly $75 \%$ ? Explain why or why not.
d. Two of the estimates of population characteristics from this study were that $75 \%$ of teens own a cell phone and that $26 \%$ of teens ages $16-17$ have used their phones to text while driving. Which of these two estimates do you think is more accurate and why? (Hint: What do you know about the number of teens surveyed?)

Rashmi Sinha
Rashmi Sinha
Numerade Educator
02:22

Problem 3

The article "More Communities Banning 'Television on a Stick"" (USA TODAY, March 23,2010 ) describes an ongoing controversy over the distraction caused by digital billboards along highways. One study mentioned in the newspaper article is described in "Effects of Advertising Billboards During Simulated Driving" (Applied Ergonomics [2010]: 1-8). In this study, 48 people made a $9 \mathrm{~km}$ drive in a driving simulator. Drivers were instructed to change lanes according to roadside lane change signs. Some of the lane changes occurred near digital billboards. What was displayed on the digital billboard changed once during the time that the billboard was visible by the driver to simulate the changing digital billboards that appear along highways. Data from this study supported the theory that the time required to respond to road signs was greater when digital billboards were present. Is the inference made one that involves estimation or one that involves hypothesis testing? (Hint: See Example 7.1.)

Niamat Khuda
Niamat Khuda
Numerade Educator
View

Problem 4

For the study described in the previous exercis answer the following questions.
a. What is the population of interest?
b. What claim was tested?
c. What additional information would you want befo deciding if it is reasonable to generalize the conclusio of this study to the population of interest?
d. Assuming that the people who participated in the stur are representative of the population of interest, do y think that the risk of an incorrect conclusion would ha been lower, about the same, or higher if 100 people $\mathrm{h}$ participated instead of $48 ?$

Rashmi Sinha
Rashmi Sinha
Numerade Educator
01:12

Problem 5

Consider the population that consists of all students enrolled at a college.
a. Give an example of a question about this population that could be answered by collecting data and using it to estimate a population characteristic.
b. Give an example of a question about this population that could be answered by collecting data and using it to test a claim about this population.

Harsh Gadhiya
Harsh Gadhiya
Numerade Educator
01:21

Problem 6

Do people better remember what they learned if they are in the same physical space where they first learned it? The authors of the paper "The Dynamics of Memory: ContextDependent Updating" (Learning \& Memory (2008): $574-579)$ asked people to learn a set of 20 unrelated objects. Two days later, these people were asked to recall the objects learned on the first day. Some of the people were asked to recall the objects in the same room where they originally learned the objects. The others were asked to recall the objects in a different room. People were assigned at random to one of these two recall conditions. The authors found that the data on the
number of objects recalled supported the claim that recall is better when people return to the original learning context. Is the inference made one that involves estimation or one that involves hypothesis testing?

Dominador Tan
Dominador Tan
Numerade Educator
01:42

Problem 7

The article "The Largest Last Supper: Depictions of Food Portions and Plate Size Increase Over the Millennium"
(International Journal of Obesity [2010]: 1-2) describes a study in which each painting in a sample of 52 paintings of $T h e$ Last Supper was analyzed by comparing the size of the food plates in the painting to the head sizes of the people in the painting. For paintings that were painted prior to the year $1500,$ the estimated average plate-to-head size ratio was smaller than this ratio for the paintings that were painted after the year $1500 .$ Is the inference made one that involves estimation or one that involves hypothesis testing?

Dominador Tan
Dominador Tan
Numerade Educator
02:14

Problem 8

For the study described in the previous exercise, answer the following questions.
a. The original sample consisted of 52 paintings. These paintings were then divided into two samples consisting of 30 painted before 1500 and 22 painted after 1500 . What are the two populations of interest?
b. What population characteristics are being estimated?
c. Suppose that the paintings selected for analysis were selected at random from all paintings that portray The Last Supper. Do you think that the estimate produced for average plate-to-head size ratio for paintings made before 1500 is likely to be less accurate than the corresponding estimate for paintings made after $1500 ?$ Explain.

Nick Johnson
Nick Johnson
Numerade Educator
01:12

Problem 9

Consider the population that consists of all employees of a large computer manufacturer.
a. Give an example of a question about this population that could be answered by collecting data and using it to estimate a population characteristic.
b. Give an example of a question about this population that could be answered by collecting data and using it to test a claim about this population.

Harsh Gadhiya
Harsh Gadhiya
Numerade Educator
02:15

Problem 10

Fans of professional soccer are probably aware that players sometimes fake injuries (called dives or flops). But how common is this practice? The articles "A Field Guide to Fakers and Floppers" (The Wall Street Journal, June 28 , 2010) and "Red Card for Faking Footballers" (Science Daily, October 10,2009 ) describe a study of deceptive behavior in soccer. Based on this study, it was possible to categorize injuries as real or fake based on movements that were characteristic of fake injuries (such as an arched back with hands raised, which is meant to attract the attention of a referee but which is not characteristic of the way people fall naturally). Data from an analysis of a sample of soccer games were then used to make the following statements:
On average, referees stop a soccer game to deal with apparent injuries 11 times per game. On average, there is less than one "real" injury per soccer game. Are the inferences made ones that involve estimation or ones that involve hypothesis testing?

Lucas Finney
Lucas Finney
Numerade Educator
00:24

Problem 11

"Want to Lose More Fat? Skip Breakfast Before Workout" (The Tribune, June 4,2010 ) is the headline of a newspaper article describing a study comparing men who did endurance training without eating before training and men who ate before training. Twenty men were assigned at random to one of two 6-week diet and exercise programs. Both groups followed a similar diet and performed the same daily morning exercise routine. Men in one group did the exercise routine prior to eating, and those in the other group ate first and then exercised. The resulting data supported the claim that those who do not eat prior to exercising burn a higher proportion of fat than those who eat before exercising. Is the inference made one that involves estimation or one that involves hypothesis testing?

Nick Johnson
Nick Johnson
Numerade Educator
View

Problem 12

For the study described in the previous exercise, answer the following questions.
a. What is the population of interest?
b. What claim was tested?
c. What additional information would you want before deciding if it is reasonable to generalize the conclusions of this study to the population of interest?
d. Assuming that the people who participated in the study are representative of the people in the population of interest, do you think that the risk of an incorrect conclusion would have been lower, about the same, or higher if 10 men had participated instead of $20 ?$

Rashmi Sinha
Rashmi Sinha
Numerade Educator