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Kokoska - Introductory Statistics, 2e (Homework)

James Finch

Statistics, section 2, Fall 2019

Instructor: Dr. Friendly

Current Score : 58 / 84

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

Last Saved : n/a Saving...  ()

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58/84 (69.0%)

  • Instructions

    Kokoska's data analysis approach in Introductory Statistics: A Problem Solving Approach, 2nd edition, published by W.H. Freeman, moves students away from formulas and number-crunching, focusing instead on how working statisticians in a variety of fields collect and analyze data and use the results to tackle real-world problems. The WebAssign component for this text engages students with immediate feedback, an interactive eBook with online resources, and a question bank of end-of-section exercises.

    Question 1 is one of many multi-part questions. In particular, it has a focus on the frequency distribution and the histogram for the data, as well as a discussion about the distribution.

    Question 2 requires the student to find the sample mean and sample median, and then compare those values.

    Question 3 presents the student with a randomized box plot and several statements to complete to describe the data.

    Question 4 features a probability scenario.

    Question 5 focuses on mean, variance, and standard deviation and the related probability implications.

    Question 6 allows the student to compare the graphs of three probability density functions. The scale of the graph is randomized so that students can receive slight variations from one another.

    Question 7 gives the student the opportunity to use the central limit theorem.

    Question 8 exhibits one of the vocabulary questions presented at the beginning of each section.

    Question 9 shows a use of hypothesis testing.

    Question 10 includes an ANOVA table for the students to complete. 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.

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. –/38 points KoIntroStat2 2.4.087. My Notes
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The quality of an automobile battery is often measured by cold cranking amps (CCA), a measure of the current supplied at 0°F. Thirty automobile batteries were randomly selected and subjected to subfreezing temperatures. The resulting CCA data are given in the following table.
62 87 303 5 259 105 197 55 99 133
122 514 90 118 324 38 31 163 75 17
339 201 76 217 65 321 144 84 46 232
(a)
Construct a frequency distribution to summarize these data. (Round your relative frequency and cumulative relative frequency to four decimal places.)
Class Frequency Relative
Frequency 		Cumulative
relative
Frequency
0–50
50–100
100–150
150–200
200–250
250–300
300–350
350–400
400–450
450–500
500–550
Draw the corresponding histogram.

(b)
Describe the shape of the distribution.
The distribution is , centered near , with variability.
(c)
Estimate the middle of the distribution, a number M such that 50% of the data are below M and 50% are above M.
M =
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2. –/4 points KoIntroStat2 3.1.013. My Notes
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Tractor trailers tend to exceed the speed limit (65 mph) on one downhill stretch of a highway in Pennsylvania. Using a radar gun, the following tractor trailer speeds (in mph) were observed.
82 66 68 69 80 62 71 74 68 60 62
68 75 66 77 74 65 71 64 68 62
(a)
Find the sample mean (in mph),
x.
 (Round your answer to four decimal places.)
mph
(b)
Find the sample median (in mph), x tilde.
mph
(c)
What do your answers to parts (a) and (b) suggest about the shape of the distribution of speeds?
Since the sample median is the sample mean, this suggests that the distribution is .
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3. –/9 points KoIntroStat2 3.4.109. My Notes
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As part of a new physical fitness program, a certain middle school records the number of sit-ups each sixth-grade student can do in one minute. A random sample for males and females was obtained and the following modified box plots were drawn.
The box-and-whisker plot has a horizontal axis numbered from 25 to 65. The box-and-whisker is also horizontal. The boxplot labeled "Males" occurs next. The left whisker is approximately 26, the left edge of the box is approximately 35, the line inside the box is approximately 39, the right edge of the box is approximately 45, and the right whisker is approximately 56. There is one outlier located at 61. The boxplot labeled "Females" occurs next. The left whisker is approximately 36, the left edge of the box is approximately 37, the line inside the box is approximately 39, the right edge of the box is approximately 41, and the right whisker is approximately 49. There is one outlier located at 50.
Describe the male and female data separately. What similarities and/or differences do the box plots suggest?
The distribution for the male data is slightly skewed, centered near , has lots of variability, and one outlier. The distribution for the female data is slightly skewed, centered near , has little variability, and one outlier. The distributions are centered and skewed. The female data appear more than the male data.
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4. –/3 points KoIntroStat2 4.4.121. My Notes
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According to Trail Count, the annual survey of San Jose's off-street bicycle and pedestrian trail users, approximately 24% use trails daily. Suppose 12% use trails daily for exercise, and 8% use trails daily for commuting. Suppose a trail user is randomly selected. (Round your answers to four decimal places.)
(a)
Given that the person uses trails daily, what is the probability that he/she uses the trails for exercise?
(b)
Given that the person uses trails daily, what is the probability that he/she uses the trails for commuting?
(c)
If the person uses trails daily, what is the probability that he/she does not use the trial for commuting?
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5. –/6 points KoIntroStat2 5.3.059. My Notes
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A bill introduced into the Virginia State Senate stipulated that the owner of a tanning facility must identify and document the skin type of every customer, and must advise every customer of the maximum time of recommended exposure in the tanning device. Past records indicate that most sessions range from 10 to 30 minutes. Suppose the duration of a tanning session (in minutes) at the Solar Planet tanning facility in a certain city is a discrete random variable with probability distribution given in the table below.
x p(x)
10 0.30
12 0.25
15 0.15
20 0.14
25 0.10
30 0.06
(a)
Find the mean, variance, and standard deviation of the duration of a tanning session time. (Round your standard deviation to four decimal places.)
mean variance standard deviation
(b)
Find the probability that a randomly selected session has a duration within one standard deviation of the mean.
(c)
Find the probability that a randomly selected session has a duration within two standard deviations of the mean.
(d)
Suppose a sunlamp lasts for 100 hours. After approximately how many tanning sessions will the sunlamp have to be replaced? (Round your answer to the nearest whole number.)
sessions
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6. –/3 points KoIntroStat2 7.2.038. My Notes
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The figure below shows graphs of the probability density function for the random variable X and the approximate density functions for the random variable
X
 for
n = 5
 and the random variable
X
 for
n = 15.
WebAssign Plot
Identify each probability density function.
The graph of the probability density function for the random variable X is . The graph of the probability density function for the random variable
X
 for
n = 5
 is . The graph of the probability density function for the random variable
X
 for
n = 15
 is .
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7. –/4 points KoIntroStat2 7.2.045. My Notes
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During monsoon season in a certain country, the mean amount of rainfall is 85 centimeters. Suppose the standard deviation is 5 centimeters and 20 monsoon seasons are selected at random.
(a)
What is the probability that the sample mean rainfall is less than 83 centimeters? (Round your answer to four decimal places.)
(b)
What is the probability that the sample mean rainfall is greater than 87.5 centimeters? (Round your answer to four decimal places.)
(c)
Find a symmetric interval about the mean, 85, such that the probability that the sample mean lies in this interval is 0.90. (Round your answers to one decimal place.)
With probability 0.90, the sample mean lies between a lower value of and an upper value of centimeters.
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8. –/1 points KoIntroStat2 8.1.005. My Notes
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Fill in the blank.
An unbiased statistic with the smallest possible variance is called the .
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9. –/4 points KoIntroStat2 9.3.083. My Notes
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Many people live under a lot of stress and various time constraints. Consequently, some people run out of the house without the keys, and are locked out. Rather than break into one's own home, most people in these circumstances call a locksmith. In 2013, the mean service charge for a locksmith was $68. A random sample of 26 locksmith service charges in certain city was obtained. The sample mean was $72.31. Assume the underlying population distribution is normal and that
σ = 15.6.
 Is there any evidence to suggest the mean locksmith service charge in this city is greater than $68? Use
α = 0.05.
State the four parts of the hypothesis test.
    
Give the value of the appropriate
zα
 or
zα/2.
 (Round your answer to four decimal places.)
Calculate the test statistic. (Round your answer to four decimal places.)
z =
What can you conclude?
    
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10. –/12 points KoIntroStat2 11.1.015. My Notes
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–/12
 
A study was conducted to compare the amount of salt in potato chips. Random samples of four varieties were obtained and the amount of salt in each one-ounce portion of potato chips was recorded (in mg of sodium). The data are given in the following table.
Variety Observations
BBQ 337 155 239 184 185 262
Cheese-Flavored 236 237 252 229 232 232
Olestra-Based 164 196 136 215 147 231
Baked 291 343 293 373 306 357
Conduct an analysis of variance test to determine whether there is any evidence that the population mean amount of salt per serving is different for at least two varieties. Use
α = 0.05.
(a)
State the four parts of the hypothesis test.
    
(b)
Complete an ANOVA table. (Use technology to find the p value. Round your p value to four decimal places and all other values to two decimal places.)
Source of
variation 		Sum of
squares 		Degrees of
freedom 		Mean
squares 		F p value
Factor
Error
Total
(c)
Draw the appropriate conclusion.
    
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