For the X,Y data compute
X 4 3 5 11 10 14
Y 6 7 12 17 9 21
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1. For the X,Y data compute:
a. r and determine if it is significantly different from zero.
b. the slope of the regression line and test if it differs significantly from zero.
c. the 95% confidence interval for the slope.
2. 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% freshman, 25% juniors, 25% sophomores, 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?
3. A geologist collects hand-specimen sized pieces of lime stone from a particular area. A qualitative assessment of both texture and color is made with the following results.
Fine: 4 light, 20 medium, 8 dark Medium: 5 light, 23 medium, 12 dark Coarse: 21 light, 23 medium, 4 dark
Is there evidence of association between color and texture for these lime stones? Explain your answer.
5. Do men and women select different breakfasts? The breakfasts ordered by randomly selecting men and women at a popular breakfast place is shown. Conduct a test for homogeneity at a 5% level of significance.
6. Can a coefficient of determination be negative? Why or why not?
7. The cost of a leading liquid laundry detergent in different sizes is given below. Size (ounces) Cost ($) 16 4 32 5 64 6 200 11
a. Is the least squares line valid for predicting what a 300 ounce size of the laundry detergent would cost? Why or why not?
b. What is the slope of the least squares (best-fit) line? Interpret the slope.
8. Use the information to answer questions a, b, c and d: 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 fights is 22 minutes with a standard deviation of 15 minutes.
a. df =
b. Let α = .05
d. Conclusion (write out in a complete sentence):
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