Posted: December 3rd, 2015

linear correlation &chi square

linear correlation &chi square

1.    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?

2.    For the X,Y data below, compute:
a. r and determine if it is signi?cantly different from zero.
b. the slope of the regression line and test if it differs signi?cantly from zero.
c. the 95% con?dence interval for the slope.
X    y
4    6
3    7
5    12
11    17
10    9
14    17

3.    At a school pep rally, a group of sophomore students organized a free raf?e

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 ?shy that

sophomores organized the raf?e 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 signi?cance 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?

4.    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.
colour
texture    Light     Medium    Dark
Fine     4    20    8
medium    5    23    12
course    21    23    4

5.    True or False ? The standard deviation of the chi-square distribution is

twice the mean.

6.    Do men and women select different breakfasts? The breakfasts ordered by

randomly selected men and women at a popular breakfast place is shown. Conduct a

test for homogeneity at a 5% level of significance
a.    H0: _______
b.    b. Ha: _______
c.    In words,clearlystate what your random variable X ¯1- X ¯2, P’1-P’2 or X ¯d

represents.
d. State the distribution to use for the test.
e. What is the test statistic?
f. What is thep-value? In one to two complete sentences, explain what the p-value

means for this problem Indicatethecorrectdecision

(“reject”or“donotreject”thenullhypothesis),thereasonforit,andwriteanappropriate

conclusion, usingcomplete sentences.
a. Alpha: _______
b. Decision: _______
c. Reason for decision: _______
d. Conclusion: _______ .
g. In complete sentences, explain how you determined which distribution to use.

7.    Supposeanairlineclaimsthatitsflightsare consistently

ontimewithanaveragedelayofatmost15minutes.Itclaimsthattheaveragedelayissoconsistent

thatthevarianceisno 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.df= ________

8.    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.Leta= 0.05 Decision: ________ Conclusion (write out in a

complete sentence.): ________

9.     Can a coefficient of determination be negative? Why or why not?

10.
Size (ounces)    Cost    Cost per ounce
6    3.99
32    4.99
64    5.99
200    10.99

a. Using “size” as the independent variable and “cost” as the dependent variable,

draw a scatter plot.

b. Does it appear from inspection that there is a relationship between the

variables? Why or why not?
c. Calculate the least-squares line. Put the equation in the form of: y=a+bx
d. Find the correlation coefficient. Is it significant?
e. If the laundry detergent were sold in a 40-ounce size, find the estimated cost.
f. If the laundry detergent were sold in a 90-ounce size, find the estimated cost.
g. Does it appear that a line is the best way to fit the data? Why or why not?
h. Are there any outliers in the given data?
i. Istheleast-squareslinevalidforpredictingwhata300-

ouncesizeofthelaundrydetergentwouldyoucost?Why or why not?
j. What is the slope of the least-squares (best-fit) line? Interpret the slope

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