Essential Statistics
Essential Statistics
2nd Edition
ISBN: 9781259570643
Author: Navidi
Publisher: MCG
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Chapter 3.2, Problem 35E

a.

To determine

Find the population standard deviation of the rating for 2007-2008.

a.

Expert Solution
Check Mark

Answer to Problem 35E

  • The population standard deviation of the ratting for 2007-2008 is 2.36.

Explanation of Solution

Calculation:

The ratings for the top 20 prime-time show for 2007-2008 and 2012-2013 seasons are given.

Standard deviation:

Let x1,x2...xN be the population observations of size N. the population mean is denoted by μ. Hence, the population standard deviation can be expressed as,

σ=(xμ)2N=x2Nμ2N

Population standard deviation:

Finding mean:

Software procedure:

Step-by-step procedure to find mean using the MINITAB software:

  • Choose Stat > Basic Statistics > Display Descriptive Statistics.
  • In Variables enter the columns Rating (2007-08).
  • Choose option statistics, and select Mean.
  • Click OK.

Output using the MINITAB software is given below:

  • Essential Statistics, Chapter 3.2, Problem 35E , additional homework tip  1
  • From the MINITAB output the mean is 10.76.

The deviation, deviation’s squares are calculated below:

x(xμ)(xμ)2
16.15.3428.5156
15.95.1426.4196
143.2410.4976
12.71.943.7636
12.61.843.3856
11.81.041.0816
11.60.840.7056
10.6–0.160.0256
10.5–0.260.0676
10.4–0.360.1296
9.7–1.061.1236
9.2–1.562.4336
9.2–1.562.4336
9.2–1.562.4336
9–1.763.0976
8.8–1.963.8416
8.8–1.963.8416
8.5–2.265.1076
8.4–2.365.5696
8.2–2.566.5536
Total(xμ)2=111.028

Substituting (xμ)2=111.028 and N = 20 in the standard deviation formula,

σ=(xμ)2N=111.02820=2.36

  • Hence, the population standard deviation of the ratting for 2007-2008 is 2.36.

b.

To determine

Find the population standard deviation of the ratting for 2012-2013.

b.

Expert Solution
Check Mark

Answer to Problem 35E

  • The population standard deviation of the ratting for 2012-2013 is 1.05.

Explanation of Solution

Calculation:

Population standard deviation:

Finding mean:

Software procedure:

Step-by-step procedure to find mean using the MINITAB software:

  • Choose Stat > Basic Statistics > Display Descriptive Statistics.
  • In Variables enter the columns Rating (2012-13).
  • Choose option statistics, and select Mean.
  • Click OK.

Output using the MINITAB software is given below:

  • Essential Statistics, Chapter 3.2, Problem 35E , additional homework tip  2
  • From the MINITAB output the mean is 4.35.

The deviation, deviation’s squares are calculated below:

x(xμ)(xμ)2
7.93.5512.6025
6.21.853.4225
5.10.750.5625
4.90.550.3025
4.60.250.0625
4.60.250.0625
4.3–0.050.0025
4.3–0.050.0025
4.1–0.250.0625
4.1–0.250.0625
4–0.350.1225
4–0.350.1225
3.9–0.450.2025
3.7–0.650.4225
3.7–0.650.4225
3.6–0.750.5625
3.6–0.750.5625
3.5–0.850.7225
3.5–0.850.7225
3.4–0.950.9025
Total(xμ)2=21.91

Substituting (xμ)2=21.91 and N = 20 in the standard deviation formula,

σ=(xμ)2N=21.9120=1.05

  • Hence, the population standard deviation of the ratting for 2012-2013 is 1.05.

c.

To determine

Find the range for the rating of both seasons.

c.

Expert Solution
Check Mark

Answer to Problem 35E

  • The range for the rating of 2007-08 is 7.9 and the range for the rating of 2012-13 seasons is 4.5.

Explanation of Solution

Calculation:

Range:

The range of a data is defined as, Largest valuesmallest value.

Range:

  • From the data of the season 2007-08 the largest rating is 16.1 and the smallest value is 8.2.
  • Therefore the range is 16.18.2=7.9.
  • From the data of the season 2012-13 the largest rating is 7.9 and the smallest value is 3.4.
  • Therefore the range is 7.93.4=4.5.
  • Thus, the range for the rating of 2007-08 is 7.9 and the range for the rating of 2012-13 seasons is 4.5.

d.

To determine

Explain whether the spread in ratings increase or decrease over the seasons based on the standard deviation.

d.

Expert Solution
Check Mark

Answer to Problem 35E

  • It can be concluded that the spreads in rating has decreased from 2007-08 to 2012-13 season.

Explanation of Solution

  • From part (a), the population standard deviation of the ratting for 2007-2008 is 2.36.
  • From part (b), the population standard deviation of the ratting for 2012-2013 is 1.05.
  • The standard deviation of the rating for 2007-2008 is more than the population standard deviation of the ratting for 2012-2013.
  • Thus, it can be concluded that the spreads in rating has decreased from 2007-08 to 2013-13 season.

e.

To determine

Explain whether the spread in ratings increase or decrease over the seasons based on the range.

e.

Expert Solution
Check Mark

Answer to Problem 35E

  • It can be concluded that the spreads in rating has decreased from 2007-08 to 2012-13 season.

Explanation of Solution

  • From part (c), the range of the ratting for 2007-2008 is 7.9.
  • From part (b), the range of the ratting for 2012-2013 is 4.5.
  • The range of the ratting for 2007-2008 is more than the range of the ratting for 2012-2013.
  • Thus, it can be concluded that the spreads in rating has decreased from 2007-08 to 2012-13 season.

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Chapter 3 Solutions

Essential Statistics

Ch. 3.1 - Prob. 11ECh. 3.1 - Prob. 12ECh. 3.1 - Prob. 13ECh. 3.1 - Prob. 14ECh. 3.1 - Prob. 15ECh. 3.1 - Prob. 16ECh. 3.1 - Prob. 17ECh. 3.1 - 18. Find the mean, median, and mode for the...Ch. 3.1 - Prob. 19ECh. 3.1 - In Exercises 19–22, use the given frequency...Ch. 3.1 - Prob. 21ECh. 3.1 - In Exercises 19–22, use the given frequency...Ch. 3.1 - Prob. 23ECh. 3.1 - Prob. 24ECh. 3.1 - Prob. 25ECh. 3.1 - Prob. 26ECh. 3.1 - Prob. 27ECh. 3.1 - Prob. 28ECh. 3.1 - Prob. 29ECh. 3.1 - 30. Mean and median height: The National Center...Ch. 3.1 - 31. Hamburgers: An ABC News story reported the...Ch. 3.1 - Prob. 32ECh. 3.1 - Prob. 33ECh. 3.1 - Prob. 34ECh. 3.1 - Prob. 35ECh. 3.1 - 36. Beer: The following table presents the number...Ch. 3.1 - Prob. 37ECh. 3.1 - Prob. 38ECh. 3.1 - 39. Heavy football players: Following are the...Ch. 3.1 - Prob. 40ECh. 3.1 - Prob. 41ECh. 3.1 - 42. News flash: The following table presents the...Ch. 3.1 - Prob. 43ECh. 3.1 - Prob. 44ECh. 3.1 - Prob. 45ECh. 3.1 - Prob. 46ECh. 3.1 - Prob. 47ECh. 3.1 - Prob. 48ECh. 3.1 - Prob. 49ECh. 3.1 - Prob. 50ECh. 3.1 - Prob. 51ECh. 3.1 - 52. Sources of news: A sample of 32 U.S. adults...Ch. 3.1 - Prob. 53ECh. 3.1 - Prob. 54ECh. 3.1 - Prob. 55ECh. 3.1 - Prob. 56ECh. 3.1 - Prob. 57ECh. 3.1 - Prob. 58ECh. 3.1 - Prob. 59ECh. 3.1 - Prob. 60ECh. 3.1 - Prob. 61ECh. 3.1 - Prob. 62ECh. 3.1 - Prob. 63ECh. 3.1 - Prob. 64ECh. 3.1 - Prob. 65ECh. 3.1 - Prob. 66ECh. 3.1 - Prob. 67ECh. 3.1 - Prob. 68ECh. 3.1 - Prob. 69ECh. 3.1 - Prob. 70ECh. 3.1 - Prob. 71ECh. 3.1 - Prob. 72ECh. 3.1 - Prob. 73ECh. 3.1 - Prob. 74ECh. 3.2 - 1. Compute the population variance for the St....Ch. 3.2 - Prob. 2CYUCh. 3.2 - Prob. 3CYUCh. 3.2 - Prob. 4CYUCh. 3.2 - Prob. 5CYUCh. 3.2 - Prob. 6CYUCh. 3.2 - Prob. 7CYUCh. 3.2 - Prob. 8CYUCh. 3.2 - Prob. 9ECh. 3.2 - In Exercises 9–12, fill in each blank with the...Ch. 3.2 - Prob. 11ECh. 3.2 - In Exercises 9–12, fill in each blank with the...Ch. 3.2 - Prob. 13ECh. 3.2 - In Exercises 13–16, determine whether the...Ch. 3.2 - Prob. 15ECh. 3.2 - Prob. 16ECh. 3.2 - Prob. 17ECh. 3.2 - 18. Find the sample variance and standard...Ch. 3.2 - Prob. 19ECh. 3.2 - Prob. 20ECh. 3.2 - Prob. 21ECh. 3.2 - Prob. 22ECh. 3.2 - 23. Approximate the sample variance and standard...Ch. 3.2 - 24. Approximate the sample variance and standard...Ch. 3.2 - Prob. 25ECh. 3.2 - Prob. 26ECh. 3.2 - Prob. 27ECh. 3.2 - Prob. 28ECh. 3.2 - Prob. 29ECh. 3.2 - Prob. 30ECh. 3.2 - Prob. 31ECh. 3.2 - Prob. 32ECh. 3.2 - 33. Heavy football players: Following are the...Ch. 3.2 - 34. Beer: The following table presents the number...Ch. 3.2 - Prob. 35ECh. 3.2 - Prob. 36ECh. 3.2 - Prob. 37ECh. 3.2 - Prob. 38ECh. 3.2 - Prob. 39ECh. 3.2 - Prob. 40ECh. 3.2 - Prob. 41ECh. 3.2 - 42. Pay your bills: In a large sample of customer...Ch. 3.2 - Prob. 43ECh. 3.2 - Prob. 44ECh. 3.2 - Prob. 45ECh. 3.2 - 46. Pay your bills: For the data in Exercise 42,...Ch. 3.2 - Prob. 47ECh. 3.2 - 48. Internet providers: For the data in Exercise...Ch. 3.2 - Prob. 49ECh. 3.2 - Prob. 50ECh. 3.2 - Prob. 51ECh. 3.2 - Prob. 52ECh. 3.2 - Prob. 53ECh. 3.2 - Prob. 54ECh. 3.2 - Prob. 55ECh. 3.2 - Prob. 56ECh. 3.2 - Prob. 57ECh. 3.2 - Prob. 58ECh. 3.2 - Prob. 59ECh. 3.2 - Prob. 60ECh. 3.2 - Prob. 61ECh. 3.2 - Prob. 62ECh. 3.2 - Prob. 63ECh. 3.3 - Following are final exam scores, arranged in...Ch. 3.3 - Prob. 2CYUCh. 3.3 - Prob. 3CYUCh. 3.3 - Prob. 4CYUCh. 3.3 - Prob. 5ECh. 3.3 - In Exercises 5–8, fill in each blank with the...Ch. 3.3 - Prob. 7ECh. 3.3 - In Exercises 5–8, fill in each blank with the...Ch. 3.3 - Prob. 9ECh. 3.3 - In Exercises 9–12, determine whether the statement...Ch. 3.3 - Prob. 11ECh. 3.3 - Prob. 12ECh. 3.3 - A population has mean μ = 7 and standard deviation...Ch. 3.3 - Prob. 14ECh. 3.3 - Prob. 15ECh. 3.3 - Prob. 16ECh. 3.3 - Prob. 17ECh. 3.3 - Prob. 18ECh. 3.3 - Prob. 19ECh. 3.3 - For the data set a. Find the 80th percentile. b....Ch. 3.3 - Standardized tests: In a recent year, the mean...Ch. 3.3 - A fish story: The mean length of one-year-old...Ch. 3.3 - Prob. 23ECh. 3.3 - Blood pressure in women: The article referred to...Ch. 3.3 - Hazardous waste: Following is a list of the number...Ch. 3.3 - Cholesterol levels: The National Health and...Ch. 3.3 - Commuting to work: Jamie drives to work every...Ch. 3.3 - Windy city by the bay: Following are wind speeds...Ch. 3.3 - Caffeine: Following are the number of grams of...Ch. 3.3 - Nuclear power: The following table presents the...Ch. 3.3 - Place your bets: Recently, 28 states in the U.S....Ch. 3.3 - Hail to the chief: There have been 57 presidential...Ch. 3.3 - Prob. 33ECh. 3.3 - Prob. 34ECh. 3.3 - Prob. 35ECh. 3.3 - Automotive emissions: Following are levels of...Ch. 3.3 - Prob. 37ECh. 3.3 - Prob. 38ECh. 3.3 - Prob. 39ECh. 3.3 - Boxplot possible? Following is the five-number...Ch. 3.3 - Unusual boxplot: Ten residents of a town were...Ch. 3.3 - Prob. 42ECh. 3.3 - The vanishing outlier: Seven families live on a...Ch. 3.3 - Prob. 44ECh. 3.3 - Prob. 45ECh. 3 - Of the mean, median, and mode, which must be a...Ch. 3 - Prob. 2CQCh. 3 - Prob. 3CQCh. 3 - Prob. 4CQCh. 3 - Prob. 5CQCh. 3 - Prob. 6CQCh. 3 - Each of the following histograms represents a data...Ch. 3 - Prob. 8CQCh. 3 - Prob. 9CQCh. 3 - Prob. 10CQCh. 3 - Prob. 11CQCh. 3 - Prob. 12CQCh. 3 - Prob. 13CQCh. 3 - Prob. 14CQCh. 3 - Prob. 15CQCh. 3 - Prob. 1RECh. 3 - Prob. 2RECh. 3 - Prob. 3RECh. 3 - Prob. 4RECh. 3 - Prob. 5RECh. 3 - Prob. 6RECh. 3 - Measure that ball: Each of 16 students measured...Ch. 3 - Prob. 8RECh. 3 - Prob. 9RECh. 3 - How long can you talk? A manufacturer of cell...Ch. 3 - Prob. 11RECh. 3 - Advertising costs: The amounts spent (in billions)...Ch. 3 - Prob. 13RECh. 3 - Prob. 14RECh. 3 - Prob. 15RECh. 3 - Prob. 1WAICh. 3 - Explain why the Empirical Rule is more useful than...Ch. 3 - Prob. 3WAICh. 3 - Prob. 4WAICh. 3 - Prob. 5WAICh. 3 - Prob. 1CSCh. 3 - Prob. 2CSCh. 3 - Prob. 3CSCh. 3 - Prob. 4CSCh. 3 - Prob. 5CSCh. 3 - Prob. 6CSCh. 3 - Prob. 7CSCh. 3 - Prob. 8CSCh. 3 - Prob. 9CS
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