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Larose - Discovering Statistics, 3/e (Homework)

James Finch

Statistics, section 2, Fall 2019

Instructor: Dr. Friendly

Current Score : 6 / 81

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

Last Saved : n/a Saving...  ()

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Question
Points
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–/5 –/4 –/1 –/6 –/11 –/8 –/13 –/6 –/27
Total
6/81 (7.4%)

  • Instructions

    Dan Larose's Discovering Statistics, 3rd edition, published by W. H. Freeman, is the ideal text for instructors who want to teach the basics of statistical computation as well as how to interpret and apply the results of those computations. Using real data, contemporary examples, step-by-step solutions, extensive pedagogy, and support for common statistical software options, the text familiarizes students with essential computational skills, while helping them build the conceptual understanding needed to interpret and explain their findings. The WebAssign component of this title features an interactive eBook, video resources and a Course Pack of premade assignments.

    Question 1 features a randomized data table where a student fills in a stem-and-leaf display based on their unique set of values.

    Question 2 demonstrates grading for the coefficients of a linear regression line, allowing for potential partial credit.

    Question 3 exhibits grading for a list of values, where the number of values is randomized and the student may enter the list in any order.

    Question 4 is a multi-part question analyzing a discrete probability distribution, then identifying outliers by selecting all appropriate values from a list.

    Question 5 has the student calculate the normal data values for a given area, and tolerance allows for the use of a table or technology. It also utilizes a graph of a normal distribution as the backdrop for labeling key values of the sampling distribution.

    Question 6 shows the format for a confidence interval and has the student interpret each part of the question.

    Question 7 includes a downloadable data set for students to analyze and perform a hypothesis test using a statistical program.

    Question 8 works through a hypothesis test for two proportions using randomized data.

    Question 9 contains an ANOVA table and hypothesis test, with tolerance that accounts for rounding intermediate values. 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. –/5 points LaroseStat3 2.2.057. My Notes
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A country currently maintains a negative trade balance with many countries around the world, meaning that it imports more from those countries than it export to them. This tends to increase unemployment there. The data in the table below represent the exports, imports, and trade balance of this country with a sample of 9 countries, for a particular month.
Exports, Imports, and Trade Balance (In $ Billions)
Country Exports To Imports
From 		Trade
Balance
Brazil 3.5 2.5 1
France 2.8 4 −1.2
Germany 3.5 10 −6.5
India 1.9 3.2 −1.3
Italy 1.2 3.7 −2.5
Japan 5.6 11.3 −5.7
South Korea 4.8 5.6 −0.8
Saudi Arabia 1.7 3.5 −1.8
United Kingdom 4.4 4.4 0
Construct a stem-and-leaf display of the Exports To data from the above table. (Use the "ones" place to represent the stem and the "tenths" decimal place to represent the leaves. Enter numbers from smallest to largest separated by spaces. Enter NONE for stems with no values.)
1
2
3
4
5
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2. –/4 points LaroseStat3 4.2.021. My Notes
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–/4
 
The heights (in inches) and weights (in pounds) of a sample of five women are recorded. (Round your answers to one decimal place.)
x = height
y = weight
66 121
67 133
69 152
68 139
65 125
(a)
Calculate the slope b1 and the y-intercept b0 of the regression line. Write the regression equation.
ŷ = x +
(b)
Interpret the values for b1 and b0.
For each increase of 1 inch, the estimated weight increases by pounds. When
x = 0 inches,
 the estimated weight is pounds.
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3. –/1 points LaroseStat3 6.1.013. My Notes
Question Part
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1
–/1
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–/1
 
Write down the possible values of the discrete random variables. (Enter your answers as a comma-separated list.)
the number of students in a classroom where the maximum class size is 11
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4. –/6 points LaroseStat3 6.1.068. My Notes
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Submissions Used
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–/6
 
A police department tracks the number of vehicles involved in each vehicle collision in a city. The table shows the frequency distribution for
X = the
 number of people injured in collisions in the city in July 2014.
X = number of injured
 		Frequency
0 3068
1 452
2 47
3 10
4 3
5 2
6 1
7 2
(a)
Calculate the expected value of the number of people injured. (Round your answer to four decimal places.)
people
Interpret the expected value of the number of people injured.
    
(b)
Compute the variance and standard deviation of the number of people injured. (Round your answers to four decimal places.)
variance people standard deviation people
(c)
Use the Z-score method to identify all outlier numbers of people injured in a collision. (Select all that apply.)

Use the Z-score method to identify all moderately unusual numbers of people injured in a collision. (Select all that apply.)

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5. –/11 points LaroseStat3 7.1.047-052. My Notes
Question Part
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Submissions Used
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Total
–/11
 
Assume that the random variable X follows a normal distribution, with mean
μ = 100
 and standard deviation
σ = 42.
 We take random samples of size
n = 49.
(a)
Calculate
μx
 and
σx.
μx = σx =
(b)
Draw a graph of the sampling distribution of
x.
 On the number line, indicate
μx,
μx − 3σx,
 and
μx + 3σx.
μx − 3σx
μx
μx + 3σx
(c)
Find the value of
x
 that is greater than 95% of all values of
x.
 (Round your answer to two decimal places.)
(d)
Without using your calculator, use the symmetry of the normal distribution to calculate the value of
x
 that is smaller than 95% of all values of
x.
 (Round your answer to two decimal places.)
(e)
In your graph, shade the middle 90% of the area under the curve.

What are the two symmetric values for the sample mean that contain the middle 90% of sample means? (Round your answers to two decimal places.)
smaller value larger value
(f)
What proportion of
x
 values lies outside the values you found in part (e)?
You may need to use the appropriate table in the Appendix of Tables to answer this question.
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6. –/8 points LaroseStat3 8.1.074. My Notes
Question Part
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–/8
 
Human exposure to herbicides is a potential hazard in America's grain-producing areas. One study found that, in a random sample of 112 homes in a state, the median concentration of the herbicide dicamba was 192.8 ng/g (nanograms per gram). Suppose that the sample mean was 193 ng/g, and assume that the population standard deviation is 20 ng/g.
(a)
Compute the margin of error E for a confidence interval with 95% confidence. (Round your answer to one decimal place.)
E = ng/g
Interpret the margin of error.
    
(b)
Construct a 95% confidence interval for the population mean concentration of the herbicide dicamba in homes in this state. (Round your answers to one decimal place.)
,
ng/g
Interpret the confidence interval.
    
(c)
How large a sample size is needed to estimate μ to within 3.7 ng/g with 95% confidence? (Round your answer up to the nearest whole number.)
homes
Comment on this sample size.
    
(d)
How large a sample size is needed to estimate μ to within 3.7 ng/g with 99% confidence? (Round your answer up to the nearest whole number.)
homes
You may need to use the appropriate table in the Appendix of Tables to answer this question.
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7. –/13 points LaroseStat3 9.2.068. My Notes
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–/13
 
Use a statistical computing package (like Minitab) to explore the data set Nutrition.
(a)
Use technology to explore the variable sodium. (Round your answers to two decimal places.)
x = s = n =
(b)
Use technology to test at level of significance
α = 0.05
 whether the population mean amount of sodium is greater than 275 mg. Let
σ = 625 mg.
 State the hypotheses.
    
Find Zcrit. (Round your answer to two decimal places.)
Zcrit =
Find the critical region.
    
Find Zdata. (Round your answer to two decimal places.)
Zdata =
State the conclusion and the interpretation.
    
(c)
Use technology to test at level of significance
α = 0.05
 whether the population mean amount of sodium is greater than 315 mg. Let
σ = 625 mg.
 State the hypotheses.
    
Find Zcrit. (Round your answer to two decimal places.)
Zcrit =
Find the critical region.
    
Find Zdata. (Round your answer to two decimal places.)
Zdata =
State the conclusion and the interpretation.
    

Supporting Materials

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8. –/6 points LaroseStat3 10.3.011. My Notes
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–/6
 
Perform a hypothesis test, at level of significance
α = 0.10,
 whether
p1 ≠ p2.
Sample 1
n1 = 524
x1 = 413
Sample 2
n2 = 616
x2 = 496
(a)
State the hypotheses.
    
State the rejection rule.
    
(b)
Calculate p̂pooled. (Round your answer to two decimal places.)
p̂pooled =
(c)
Calculate Zdata. (Round your answer to two decimal places.)
Zdata =
(d)
Calculate the p-value. (Round your answer to four decimal places.)
p-value =
(e)
Compare the p-value with α. State and interpret your conclusion.
    
You may need to use the appropriate table in the Appendix of Tables to answer this question.
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9. –/27 points LaroseStat3 12.1.033. My Notes
Question Part
Points
Submissions Used
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0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100
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–/27
 
Assume that the data are independently drawn random samples from normal populations.
A study looked at body measurements for physically fit males and females. Is there a difference in weight among different age groups? The table contains the weights of five randomly chosen females from each of three age groups: younger (18–22), middle (23–30), and older (31+).
Younger Middle Older
119 142.9 121.3
124.8 104.3 107.4
130.7 115.1 169.3
130.1 98.8 122.8
155.4 110.4 155.8
(a)
Verify the equal-variance assumption.
Calculate the standard deviations s. (Round your answers to two decimal places.)
sYounger sMiddle sOlder
What can you conclude?
The largest standard deviation larger than twice the smallest standard deviation, so the equal variance requirement satisfied.
(b)
Calculate the following measures. (Round your answers to two decimal places.)
(i)
df1 and df2
df1 df2
(ii)
x double bar
(iii)
SSTR
(iv)
SSE
(v)
SST
(vi)
MSTR
(vii)
MSE
(viii)
 Fdata
(c)
Construct the ANOVA table. (Round your answers to two decimal places.)
Source of
variation 		Sum of
squares 		Degrees of
freedom 		Mean
squares 		F-test statistic
Treatment
Error
Total
(d)
Perform the appropriate one-way ANOVA using level of significance
α = 0.05.
State the hypotheses.
    
State the rejection rule.
    
Find Fdata. (Round your answer to two decimal places.)
Fdata =
Find the p-value. (Round your answer to four decimal places.)
p-value =
State the conclusion and interpretation.
    
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