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UMUC STAT-200 Homework Assignments Week #7

Textbook #1: Lane et al. Introduction to Statistics, David M. Lane et al., 2013.
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Textbook #2:Illowsky et al. Introductory Statistics, Barbara Illowsky et al., 2013.

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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.

Lane – Chapter 14: (2,6)

2. The formula for a regression equation is Y’ = 2X + 9.

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 (X,Y) data points below, compute:

Data Points: (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 (a=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. Leta=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”.

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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