Solved by verified expert:PLease show all workTextbook #1: Lane et al. Introduction to Statistics, David M. Lane et al., 2013. ( http://onlinestatbook.com/Online_Statistics_Educat… ) Textbook #2: Illowsky et al. Introductory Statistics, Barbara Illowsky et al., 2013. ( http://openstaxcollege.org/files/textbook_version/… )
umuc_stat200_hw_week7.docx
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UMUC STAT-200 Homework Assignments
Dr. Brian Killough
Week #7
Textbook #1: Lane et al.
Introduction to Statistics, David M. Lane et al., 2013.
( http://onlinestatbook.com/Online_Statistics_Education.pdf )
Textbook #2: Illowsky et al. Introductory Statistics, Barbara Illowsky et al., 2013.
( http://openstaxcollege.org/files/textbook_version/hi_res_pdf/15/col11562-op.pdf )
See the file named “UMUC_STAT200_EXCEL_Tips” at the “Course Materials” menu link to find
functions for calculating Linear Regression and Chi Square Distribution statistics.
For problems Lane #14 and Illowsky #102, you can use the following online tool to evaluate the ChiSquare statistic, degrees of freedom and probability values: http://vassarstats.net/newcs.html
Instructions: There are a total of 10 problems. In order to receive full credit (100%), students must make
a reasonable attempt at every problem and show all of their work. In some cases, a simple answer is all
that is required. If the solution requires some work, then you will need to include that work in your
submission. If you are using EXCEL to find a solution, it is acceptable to just include the formula that
was used for the solution. Just submitting an answer without any work is unacceptable and may not
receive credit.
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Lane – Chapter 14: (2,6)
2. The formula for a regression equation is Y’ = 2X + 9, where Y’ is the predicted score.
a. What would be the predicted score for a person scoring 6 on X?
b. If someone’s predicted score was 14, what was this person’s score on X?
6. For the given (X,Y) data points, compute: (4,6), (3,7), (5,12), (11,17), (10,9), (14,21)
a. The correlation (r) and determine if it is significantly different from a hypothesized slope of 0 (null
hypothesis). HINT: Use the significance test for correlation on Page-482 and assume a 95% confidence.
b. The slope and intercept of the linear regression line
Lane – Chapter 17: (5,14)
5. At a school pep rally, a group of sophomore students organized a free raffle for prizes. They claim that
they put the names of all of the students in the school in the basket and that they randomly drew 36 names
out of this basket. Of the prize winners, 6 were freshmen, 14 were sophomores, 9 were juniors, and 7 were
seniors. The results do not seem that random to you. You think it is a little fishy that sophomores
organized the raffle and also won the most prizes. Your school is composed of 30% freshmen, 25%
sophomores, 25% juniors, and 20% seniors.
a. What are the expected frequencies of winners from each class?
b. Conduct a significance test to determine whether the winners of the prizes were distributed throughout
the classes as would be expected based on the percentage of students in each group. Report your Chi
Square and p values.
c. What do you conclude about the null hypothesis (the observed and expected data are the same)
assuming a 95% confidence?
14. A geologist collects hand-specimen sized pieces of limestone
from a particular area. A qualitative assessment of both texture and
color is made with the following results. Is there evidence of
association between color and texture for these limestones? Explain
your answer by testing your null hypothesis assuming a 95%
confidence level.
Illowsky – Chapter 11 (70,102,113,117)
70. TRUE or FALSE … The standard deviation of the chi-square distribution is twice the mean.
102. Do men and women select different breakfasts? The breakfasts ordered by randomly selected men
and women at a popular breakfast place is shown in the table. Conduct a test for homogeneity at a 5%
level of significance (=0.05).
Suppose an airline claims that its flights are consistently on time with an average delay of at most 15
minutes. It claims that the average delay is so consistent that the variance is no more than 150 minutes.
Doubting the consistency part of the claim, a disgruntled traveler calculates the delays for his next
25 flights. The average delay for those 25 flights is 22 minutes with a standard deviation of 15 minutes.
113. Find df
117. Let =0.05. What is your decision regarding the hypothesis? Write your conclusion in a sentence
and discuss whether there is sufficient data to support your decision. HINT: See Section 11.6 on “Test of
a Single Variance”. An answer is not sufficent … you need to show your work on how you calculated the
test statistic and p-value.
Illowsky – Chapter 12 (66,82)
66. Can a coefficient of determination be negative? Why or why not?
82. The cost of a leading liquid laundry detergent in different sizes is given in the table.
a. Using “size” as the independent variable (x) and “cost” as the dependent variable (y), and draw a scatter
plot using EXCEL.
b. Calculate the least-squares line. Put the equation in the form of: ŷ = a + bx. See the instructors
“EXCEL Tips” for finding a linear regression.
c. Find the correlation coefficient. Is it significant?
d. If the laundry detergent were sold in a 40-ounce size, find the estimated cost.
e. Is the least-squares line valid for predicting what a 300-ounce size of the laundry detergent would you
cost? Why or why not?
f. What is the slope of the least-squares (best-fit) line? Interpret the slope.
…
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