Introduction To Probability And Statistics
15th Edition
ISBN: 9781337554428
Author: Mendenhall, William.
Publisher: Cengage Learning,
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Textbook Question
Chapter 2, Problem 1RWYL
Raisins The number of raisins in each of 14miniboxes (1/2 -ounce size) was counted for ageneric brand and for Sunmaid brand raisins. Thetwo data sets are shown here:
a. What are the
b. What are the mean and the standard deviation for theSunmaid brand?
c. Compare the centers and variabilities of the twobrands using the results of parts a and b.
Expert Solution
To determine
(a)
To find:
The mean and standard deviation for the generic brand.
Answer to Problem 1RWYL
The mean and standard deviation for the generic brand are
Explanation of Solution
Given information:
The given data is,
| Generic Brand | Sunmaid | ||||||
| 25 | 26 | 25 | 28 | 25 | 29 | 24 | 24 |
| 26 | 28 | 28 | 27 | 28 | 24 | 28 | 22 |
| 26 | 27 | 24 | 25 | 25 | 28 | 30 | 27 |
| 26 | 26 | 28 | 24 | ||||
Calculation:
The data with calculation is shown in table below.
| 25 | 1.464 1 | |
| 26 | 0.044 1 | |
| 26 | 0.044 1 | |
| 26 | 0.044 1 | |
| 26 | 0.044 1 | |
| 28 | 3.204 1 | |
| 27 | 0.624 1 | |
| 26 | 0.044 1 | |
| 25 | 1.464 1 | |
| 28 | 3.204 1 | |
| 24 | 4.884 1 | |
| 28 | 3.204 1 | |
| 27 | 0.624 1 | |
| 25 | 1.464 1 | |
| Total | 367 | 20.3574 |
Table-1
The sample size is
The mean is,
The standard deviation is,
Therefore, the mean and standard deviation for the generic brand are
Expert Solution
To determine
(b)
To find:
The mean and standard deviation for Sunmaid.
Answer to Problem 1RWYL
The mean and standard deviation for the generic brand are
Explanation of Solution
Given information:
The given data is,
| Generic Brand | Sunmaid | ||||||
| 25 | 26 | 25 | 28 | 25 | 29 | 24 | 24 |
| 26 | 28 | 28 | 27 | 28 | 24 | 28 | 22 |
| 26 | 27 | 24 | 25 | 25 | 28 | 30 | 27 |
| 26 | 26 | 28 | 24 | ||||
Calculation:
The data with calculation is shown in table below.
| 25 | 1.2996 | |
| 28 | 3.4596 | |
| 25 | 1.2996 | |
| 28 | 3.4596 | |
| 29 | 8.1796 | |
| 24 | 4.5796 | |
| 28 | 3.4596 | |
| 24 | 4.5796 | |
| 24 | 4.5796 | |
| 28 | 3.4596 | |
| 30 | 14.8996 | |
| 24 | 4.5796 | |
| 22 | 17.1396 | |
| 27 | 0.7396 | |
| Total | 366 | 75.7144 |
Table-2
The sample size is
The mean is,
The standard deviation is,
Therefore, the mean and standard deviation for the generic brand are
Expert Solution
To determine
(c)
To compare:
The centers and variability of the brands.
Explanation of Solution
Given information:
The given data is,
| Generic Brand | Sunmaid | ||||||
| 25 | 26 | 25 | 28 | 25 | 29 | 24 | 24 |
| 26 | 28 | 28 | 27 | 28 | 24 | 28 | 22 |
| 26 | 27 | 24 | 25 | 25 | 28 | 30 | 27 |
| 26 | 26 | 28 | 24 | ||||
The generic brand has smaller standard of deviation as compared to Sunmaid and the mean of generic brand is greater as compared to Sunmaid.
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Examine the Variables: Carefully review and note the names of all variables in the dataset. Examples of these variables include:
Mileage (mpg)
Number of Cylinders (cyl)
Displacement (disp)
Horsepower (hp)
Research: Google to understand these variables.
Statistical Analysis: Select mpg variable, and perform the following statistical tests. Once you are done with these tests using mpg variable, repeat the same with hp
Mean
Median
First Quartile (Q1)
Second Quartile (Q2)
Third Quartile (Q3)
Fourth Quartile (Q4)
10th Percentile
70th Percentile
Skewness
Kurtosis
Document Your Results:
In RStudio: Before running each statistical test, provide a heading in the format shown at the bottom. “# Mean of mileage – Your name’s command”
In Microsoft Word: Once you've completed all tests, take a screenshot of your results in RStudio and paste it into a Microsoft Word document. Make sure that snapshots are very clear. You will need multiple snapshots. Also transfer these results to the…
Examine the Variables: Carefully review and note the names of all variables in the dataset. Examples of these variables include:
Mileage (mpg)
Number of Cylinders (cyl)
Displacement (disp)
Horsepower (hp)
Research: Google to understand these variables.
Statistical Analysis: Select mpg variable, and perform the following statistical tests. Once you are done with these tests using mpg variable, repeat the same with hp
Mean
Median
First Quartile (Q1)
Second Quartile (Q2)
Third Quartile (Q3)
Fourth Quartile (Q4)
10th Percentile
70th Percentile
Skewness
Kurtosis
Document Your Results:
In RStudio: Before running each statistical test, provide a heading in the format shown at the bottom. “# Mean of mileage – Your name’s command”
In Microsoft Word: Once you've completed all tests, take a screenshot of your results in RStudio and paste it into a Microsoft Word document. Make sure that snapshots are very clear. You will need multiple snapshots. Also transfer these results to the…
Chapter 2 Solutions
Introduction To Probability And Statistics
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Ch. 2.1 - Prob. 11ECh. 2.1 - Prob. 12ECh. 2.1 - Prob. 13ECh. 2.1 - Prob. 14ECh. 2.1 - Prob. 15ECh. 2.1 - Prob. 16ECh. 2.1 - Prob. 17ECh. 2.1 - Fortune 500 Revenues Ten of the...Ch. 2.1 - Prob. 19ECh. 2.1 - Prob. 20ECh. 2.1 - Prob. 21ECh. 2.1 - Prob. 22ECh. 2.2 - Calculating the Standard Deviation I For the data...Ch. 2.2 - Calculating the Standard Deviation I For the data...Ch. 2.2 - Calculating the Standard Deviation I For the data...Ch. 2.2 - Prob. 4ECh. 2.2 - Prob. 5ECh. 2.2 - Prob. 6ECh. 2.2 - Prob. 7ECh. 2.2 - Prob. 8ECh. 2.2 - For the data sets in Exercises 79, find the range,...Ch. 2.2 - Prob. 10ECh. 2.2 - Prob. 11ECh. 2.2 - Sleep and the College Student A group of 10...Ch. 2.2 - Gas Mileage The miles per gallon (mpg) foreach of...Ch. 2.2 - Polluted Seawater Petroleum pollution in seas...Ch. 2.2 - Prob. 15ECh. 2.3 - Approximating the Standard Deviation For the data...Ch. 2.3 - Approximating the Standard Deviation For the data...Ch. 2.3 - Prob. 3ECh. 2.3 - Prob. 4ECh. 2.3 - Prob. 5ECh. 2.3 - Data Set I A distribution of measurements is...Ch. 2.3 - Prob. 7ECh. 2.3 - Data Set I A distribution of measurements is...Ch. 2.3 - Prob. 9ECh. 2.3 - Prob. 10ECh. 2.3 - Prob. 11ECh. 2.3 - Prob. 12ECh. 2.3 - Data Set II A distribution of measurements has a...Ch. 2.3 - Prob. 14ECh. 2.3 - Prob. 15ECh. 2.3 - Prob. 16ECh. 2.3 - Prob. 17ECh. 2.3 - Prob. 18ECh. 2.3 - Prob. 19ECh. 2.3 - Breathing Rates Breathing rates for humans canbe...Ch. 2.3 - Prob. 21ECh. 2.3 - Prob. 22ECh. 2.3 - Prob. 23ECh. 2.3 - Prob. 24ECh. 2.3 - Prob. 25ECh. 2.3 - Prob. 26ECh. 2.3 - Prob. 27ECh. 2.3 - Prob. 28ECh. 2.3 - Prob. 29ECh. 2.3 - Prob. 30ECh. 2.3 - Prob. 31ECh. 2.3 - TV Commercials The mean duration of...Ch. 2.4 - z-ScoresFor the data sets in Exercises 13, find...Ch. 2.4 - z-ScoresFor the data sets in Exercises 13, find...Ch. 2.4 - z-ScoresFor the data sets in Exercises 13, find...Ch. 2.4 - Median and Quartiles For the data in Exercises 46,...Ch. 2.4 - Median and Quartiles For the data in Exercises 46,...Ch. 2.4 - Median and Quartiles For the data in Exercises 46,...Ch. 2.4 - -Number Summary and the Box Plot For each of the...Ch. 2.4 - Five-Number Summary and the Box Plot For each of...Ch. 2.4 - Five-Number Summary and the Box Plot For each of...Ch. 2.4 - Prob. 10ECh. 2.4 - z-Scores vs. Box Plots For the data sets in...Ch. 2.4 - Percentiles What are the percentiles in Exercises...Ch. 2.4 - Percentiles What are the percentiles in Exercises...Ch. 2.4 - Percentiles What are the percentiles in Exercises...Ch. 2.4 - Percentiles What are the percentiles in Exercises...Ch. 2.4 - For the data in Exercises 1617, find the sample...Ch. 2.4 - For the data in Exercises 1617, find the sample...Ch. 2.4 - €For the data in Exercises 1819, find the...Ch. 2.4 - For the data in Exercises 1819, find the...Ch. 2.4 - Prob. 20ECh. 2.4 - Prob. 21ECh. 2.4 - Presidential Vetoes The number of vetoesused by...Ch. 2.4 - Prob. 23ECh. 2.4 - Prob. 24ECh. 2.4 - Ages of Pennies Here are the ages of50 pennies,...Ch. 2.4 - Prob. 26ECh. 2 - Raisins The number of raisins in each of...Ch. 2 - Raisins, continued Refer to Exercise 1. a. Find...Ch. 2 - Prob. 3RWYLCh. 2 - Prob. 4RWYLCh. 2 - Prob. 5RWYLCh. 2 - Prob. 6RWYLCh. 2 - Prob. 7RWYLCh. 2 - Prob. 8RWYLCh. 2 - Prob. 9RWYLCh. 2 - Prob. 10RWYLCh. 2 - Prob. 11RWYLCh. 2 - Prob. 12RWYLCh. 2 - Prob. 13RWYLCh. 2 - Prob. 14RWYLCh. 2 - Prob. 15RWYLCh. 2 - Prob. 16RWYLCh. 2 - Prob. 17RWYLCh. 2 - Prob. 18RWYLCh. 2 - Prob. 19RWYLCh. 2 - Prob. 20RWYLCh. 2 - Prob. 21RWYLCh. 2 - Prob. 22RWYLCh. 2 - Prob. 23RWYLCh. 2 - Prob. 24RWYLCh. 2 - Prob. 25RWYL
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