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Chapter 2: Q79E (page 111)

Parents Against Watching Television.A society called Parents Against Watching Television (PAWT) is primarily concerned with the amount of television viewed by today’s youth. It asked 300 parents of elementary school aged children to estimate the number of hours their child spent watching television in any given week. The mean and the standard deviation for their responses were 17 and 3, respectively. PAWT then constructed a stem-and-leaf display for the data, which showed that the distribution of the number of hours was a symmetric, mound-shaped distribution. Identify the interval where you believe approximately 95% of the television viewing times fell in the distribution.

Short Answer

Expert verified

11 to 23 hours is the interval where 95% of viewing time falls.

Step by step solution

01

Identifying the interval where approx. 95% of television viewing time fell

We have the mean and standard deviation as 17 and 3, respectively.

According to the Empirical Rule, 95% of measurements fall between the 2 standard deviation from mean. Therefore, we have the value of k.

Now we will use the values of mean, s and k to find the intervals.

x¯±2sUpperrange=x¯+2s=17+2(3)=17+6=23Lowerrange=x¯-2s=17-2(3)=17-6=11

Therefore, 95% of the television viewing time falls between 11 to 23 hours.

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Most popular questions from this chapter

Microsoft program security issues. To help its users combat malicious attacks (e.g., worms, viruses) on its computer software, Microsoft periodically issues a security bulletin that reports the software affected by the vulnerability. In Computers & Security (July 2013), researchers focused on reported security issues with three Microsoft products: Office, Windows, and Explorer

a. In a sample of 50 security bulletins issued in a recent year, 32 reported a security issue with Windows, 6 with Explorer, and 12 with Office. Construct a pie chart to describe the Microsoft products with security issues. Which product had the lowest proportion of security issues?

b. The researchers also categorized the security bulletins according to the expected repercussion of the vulnerability. Categories were Denial of service, Information disclosure, Remote code execution, Spoofing, and Privilege elevation. Suppose that of the 50 bulletins sampled, the following numbers of bulletins were classified into each respective category: 6, 8, 22, 3, 11. Construct a Pareto diagram to describe the expected repercussions from security issues. Based on the graph, what repercussion would you advise Microsoft to focus on?

Question: Construct a scatterplot for the data in the following table.

Variable 1: 5 1 1.5 2 2.5 3 3.5 4 4.5 5

Variable 2: 2 1 3 4 6 10 9 12 17 17

Rankings of research universities.Based on factors (e.g., academic reputation, financial aid offerings, overall cost, and success of graduates in the post-college job market) that actual college freshmen said were most important to their college decision, College Choice developed their 2015 Rankings of National Research Universities. Data for the top 50 universities are saved in the TOPUNIVfile. Several are listed in the accompanying table above.

a) The average financial aid awarded values were determined by recording the financial aid awarded to each freshman who attended the university in 2015. Does this statistic represent a population or sample mean? Interpret this value for Harvard University.

b) The median salary during early career values were determined by recording the salaries of a random selection of alumni with 0 to 5 years of experience. Does this statistic represent a population or sample median? Interpret this value for Harvard University.

Rank

University

Public/

Private

Academic Reputation Score

(100 pt. scale)

Average Financial Aid Awarded

Average Net Cost Attend

Median Salary During Early Career

% High Meaning

%Stem Degrees

1

Harvard University

Private

99

\(41,555

\)14,455

\(61,400

65%

28%

5

Yale University

Private

97

\)39,771

\(18,479

\)60,300

68%

21%

20

University of

California Berkeley

Public

79

\(16,141

\)16,178

\(59,500

50%

31%

23

University of Virginia

Public

76

\)16,834

\(12,672

\)54,700

52%

24%

27

Carnegie Mellon

University

Private

76

\(24,263

\)33,257

\(64,700

46%

51%

47

Pepperdine University

Private

60

\)29,926

\(25,345

\)48,300

51%

4%

Calculate the variance and standard deviation for samples where

a.n= 10, ∑x2 = 84, ∑x= 20

b.n= 40, ∑x2 = 380, ∑x= 100

c.n= 20, ∑x2 = 18, ∑x= 17.

Do social robots walk or roll?Refer to the International Conference on Social Robotics(Vol. 6414, 2010) study onthe current trend in the design of social robots, Exercise 2.5(p. 72). Recall that in a random sample of social robotsobtained through a Web search, 28 were built with wheels.The number of wheels on each of the 28 robots is listed inthe accompanying table.

(4 4 3 3 3 6 4 2 2 2 1 3 3 3 3 4 4 3 2 8 2 2 3 4 3 3 4 2)

Source:Based on S. Chew et al., “Do Social Robots Walk or Roll?” International Conference on Social Robotics, Vol. 6414, 2010 (adapted from Figure 2).

a.Generate a histogram for the sample data set. Is the distribution of number of wheels mound-shaped and symmetric?

b.Find the mean and standard deviation for the sample data set.

c.Form the interval, xbar ±2s.

d.According to Chebychev’s Rule, what proportion of sample observations will fall within the interval, part c?

e.According to the Empirical Rule, what proportion of sample observations will fall within the interval, part c?

f.Determine the actual proportion of sample observations that fall within the interval, part c. Even though the histogram, part a, is not perfectly symmetric, does the Empirical Rule provide a good estimate of the proportion?
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