Expert answer:Mastery exercise

  

Solved by verified expert:Please see attached the Word Document, there are 15 questions. I believe you can answer them on the same word document.Let me know if you need anything?
mth156__06_01_19__mastery_exercise_2.docx

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Q1.
Consider a sample with data values of 26, 24, 23, 17, 30, 35, 28, and 24. Compute the 20th, 25th, 65th,
and 75th percentiles (to 1 decimal, if decimals are necessary).
20th percentile?
25th percentile?
65th percentile?
75th percentile?
Q2.
The results of a national survey showed that on average, adults sleep 6.9 hours per night. Suppose that
the standard deviation is 1.3 hours.
Round your answers to the nearest whole number.
a) Use Chebyshev’s theorem to calculate the percentage of individuals who sleep between 4.3
and 9.5 hours. At least ___________ %
b) Use Chebyshev’s theorem to calculate the percentage of individuals who sleep between 3.9
and 9.9 hours. At least ___________ %
c) Assume that the number of hours of sleep follows a bell-shaped distribution. Use the
empirical rule to calculate the percentage of individuals who sleep between 4.3 and 9.5
hours per day.
__________ %
How does this result compare to the value that you obtained using Chebyshev’s theorem in
part (a)?
Select which answer:
1) The empirical rule produces a larger percentage than Chebychev’s theorem.
2) Chebyshev’s theorem produces a larger percentage than the empirical rule.
3) Or, both methods produce the same percentage.
Q3.
Scores turned in by an amateur golfer at the Bonita Fairways Golf Course in Bonita Springs, Florida,
during 2011 and 2012 are as follows:
a.
2011 Season
76 80 81 79 77 75 77 79
2012 Season
73 72 77 79 87 82 73 81
Calculate the mean (to the nearest whole number) and the standard deviation (to 2 decimals) of the
golfer’s scores, for both years.
2011
Mean
Standard deviation
2012
Mean
Standard deviation
What is the primary difference in performance between 2011 and 2012?
Select:
a)
The mean score was higher in 2011
b) The mean score was higher in 2012
c) The variation in scores was higher in 2011
d) The variation in scores was higher in 2012
What improvement, if any, can be seen in the 2012 scores?
Select:
a)
The golfer’s consistency increased in 2012
b) In 2012, three of the eight scores were better (lower) than the best score of 2011
c) There is no improvement to be seen in the 2012 scores.
Q4.
In automobile mileage and gasoline-consumption testing, 13 automobiles were road tested for 300
miles in both city and highway driving conditions. The following data were recorded for miles-pergallon performance.
City:
19.2
19.7
18.9
17.4
16.2
18.3
19.8
19
19.1
18.3
18.2
18.3
19.2
Highway:
22.6 23.8 21.5 21.8 22.4 20.6 20.4 21.8 22.2 24.3 22.6 21.7 21.9
Calculate the mean, median, and mode for City and Highway gasoline consumption (to 1 decimal).
City
Mean
Highway
Median
Mode
– Select your answ er –
Make a statement about the difference in gasoline consumption between both driving conditions.
– Select your answ er –
Q5.
Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28, and 25.
Which box plot most accurately represents these data?
Select
Q6.
Data collected by the Oil Price Information Service from more than 90,000 gasoline and convenience
stores throughout the U.S. showed that the average price for a gallon of unleaded gasoline was $3.28
(MSN Auto website, February 2, 2014). The following data show the price per gallon ($) for a sample
of 20 gasoline and convenience stores located in San Francisco.
a. Use the sample data to estimate the mean price for a gallon of unleaded gasoline in San Francisco
(to 2 decimals).
b. Compute the sample standard deviation (to 4 decimals).
c. Compare the mean price per gallon for the sample data to the national average price. What
conclusions can you draw about the cost living in San Francisco?
The input in the box below will not be graded, but may be reviewed and considered by your instructor.
Q7.
Fortune magazine’s list of the world’s most admired companies for 2014 is provided the data
contained in the WEBfile named AdmiredCompanies (Fortune, March 17, 2014). The data in the
column labelled Return shows the one-year total return (%) for the top ranked 50 companies. For the
same time period the S&P average return was 18.4%. Click on the webfile logo to reference the data.
a. Compute the median return for the top ranked 50 companies (to 1 decimal).
%
b. What percentage of the top-ranked 50 companies had a one-year return greater than the S&P
average return?
%
c. Develop the five-number summary for the data. If required, round your answers to two decimals
places. If required, enter negative values as negative numbers.
Return
Minimum
First Quartile
Median
Third Quartile
Maximum
IQR
1.5(IQR)
Lower Limit
Upper Limit
d. Are there any outliers?
– Select your answ er –
e. Select a box plot for the one year – total return.
1.
2.
3.
4.
Select the correct box plot:
– Select your answ er –
Q8.
The Wall Street Journal reported that Walmart Stores Inc. is planning to lay off 2,300 employees at
its Sam’s Club warehouse unit. Approximately half of the layoffs will be hourly employees (The Wall
Street Journal, January 25-26, 2014). Suppose the following data represent the percentage of
hourly employees laid off for 15 Sam’s Club stores.
55
56
44
43
44
56
60
62
57
45
a. Compute the mean and median percentage of hourly employees being laid off at these stores.
Mean
36
Median
b. Compute the first and third quartiles.
First quartile
Third quartile
c. Compute the range and interquartile range.
Range
Interquartile range
d. Compute the variance and standard deviation. Round your answers to four decimal places.
Variance
Standard deviation
e. Do the data contain any outliers?
– Select your answ er –
f. Based on the sample data, does it appear that Walmart is meeting its goal for reducing the
number of hourly employees?
– Select your answ er –
Q9.
According to a Los Angeles Times study of more than 1 million medical dispatches from 2007 to 2012,
the 911 response time for medical aid varies dramatically across Los Angeles. (LA Times website,
November 2012). Under national standards adopted by the Los Angeles Fire Department, rescuers are
supposed to arrive within six minutes to almost all medical emergencies. But the Times analysis found
that in affluent hillside communities stretching from Griffith Park to Pacific Palisades, firefighters failed
to hit that mark nearly 85% of the time.
The following data show the response times, in minutes, for 10 emergency calls in the Griffith Park
neighborhood.
11.8
10.3
10.7
10.6
11.5
8.3
10.5
Based on this sample of ten response times, compute the following descriptive statistics:
a. Mean, median, and mode
Mean
(to 2 decimals)
Median
(to 1 decimal)
Mode
(to 1 decimal)
b. Range and standard deviation
Range
(to 1 decimal)
Standard deviation
(to 4 decimals)
c. Should the response time of 8.3 minutes be considered an outlier in comparison to the other
response times?
– Select your answ er –
This observation
appear to be an outlier.
d. Do the response times indicate that the city is meeting the national standards?
– Select your answ er –
10.9
1
Should the city consider making changes to its response strategies?
– Select your answ er –
Would adding more stations to areas in the city be a practical solution?
– Select your answ er –
Q10.
USA Today reports that NCAA colleges and universities are paying higher salaries to a newly recruited
football coach compared to what they paid their previous football coach. (USA Today, February 12,
2013). The annual base salaries for the previous head football coach and the new head football coach
at 23 schools are given in the file Coaches. Click on the webfile logo to reference the data.
a. Determine the median annual salary for a previous head football coach and a new head football
coach
Previous Coach Median
New Coach Median
b. Compute the range for salaries for both previous and new head football coaches
Previous Coach Base
New Coach Base
c. Compute the standard deviation for salaries for both previous and new head football coaches (to 2
decimals).
Previous Coach Base
New Coach Base
d. Based on your answers to (a) to (c), comment on any differences between the annual base salary
a school pays a new head football coach compared to what it paid its pervious head football coach.
– Select your answ er –
Q11.
A random sample of 30 colleges from kiplinger’s list of the best values in private college provided the
data shown in the WEBfile named BestPrivateColleges (kiplinger, October 2013). The variable named
Admit Rate (%) shows the percentage of students that applied to the college and were admitted, and
the variable named 4-yr Grad. Rate (%) shows the percentage of students that were admitted and
graduated in four years. Click on the webfile logo to reference the data.
a. Select a scatter diagram with Admit Rate (%) as the independent variable.
1.
2.
3.
4.
Select the scatter diagram:
– Select your answ er –
What does the scatter diagram indicate about the relationship between the two variables?
– Select your answ er –
b. Compute the sample correlation coefficient. Round your answer to two decimal places and enter
negative values as negative numbers, if necessary.
What does the value of the sample correlation coefficient indicate about the relationship between the
Admit Rate (%) and the 4-yr Grad. Rate (%)?
– Select your answ er –
Q12.
Annual sales, in millions of dollars, for 21 pharmaceutical companies follow.
8,156
1,333 1,816 8,613 2,385 11,071
590 14,138 6,258 1,795 2,733
10,183
3,543
a.
7,254 3,898 4,211
717
1,315
2,063
5,620 8,056
Provide a five-number summary. If needed, round your answer to a whole number.
Smallest value
First quartile
Median
Third quartile
Largest value
b.
c.
Compute the lower and upper limits. Enter negative amounts with a minus sign.
Lower limit
Upper limit
d.
e.
Do the data contain any outliers?
– Select your answ er –
f.
Johnson & Johnson’s sales are the largest on the list at $14,138 million. Suppose a data entry error (a
transposition) had been made and the sales had been entered as $41,138 million. Would the method
of detecting outliers in part (c) identify this problem and allow for correction of the data entry error?
– Select your answ er –
g.
Which of the following box plots accurately displays the data set?
– Select your answ er –
Q13.
Five observations taken for two variables follow.
xi
yi
a.
4 6 10 5 15
40 50 30 60 30
Which of the following scatter diagrams accurately represents the data set?
1.
2.
3.
Select
b.
What does the scatter diagram developed in part (a) indicate about the relationship between the
two variables?
Select
c.
Compute the sample covariance.
d.
Compute the sample correlation coefficient (to 3 decimals).
What can you conclude, based on your computation of the sample correlation coefficient?
Select
Q14.
Consider the following data and corresponding weights.
xi
Weight(wi)
3.3
7
4.0
3
1.5
1
4.0
9
a. Compute the weighted mean (to 3 decimals).
b. Compute the sample mean of the four data values without weighting (to 3 decimals).
Q15.
The Panama Railroad Company was established in 1850 to construct a railroad across the isthmus that
would allow fast and easy access between the Atlantic and Pacific oceans. The following table provides
annual returns for Panama Railroad stock from 1853 through 1880 (The Big Ditch, Mauer and Yu,
2011). Click on the webfile logo to reference the data.
a. Select a graph of the annual returns on the stock. The New York Stock Exchange earned an annual
average return of 8.4% from 1853 through 1880.
– Select your answ er –
Can you tell from the graph if the Panama Railroad Company stock outperformed the New York Stock
Exchange?
– Select your answ er –
b. Calculate the mean annual return on Panama Railroad Company stock from 1853 through 1880.
Round your answer to one decimal place.
%
Did the stock outperform the New York Stock Exchange over the same period?
– Select your answ er –

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