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.
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X
|
Y
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|
4
|
6
|
|
3
|
7
|
|
5
|
12
|
|
11
|
17
|
|
10
|
9
|
|
14
|
21
|
Lane - Ch. 17
3. At a school pep rally, a group of sophomore students organized a free 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.
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COLOR
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COLOR
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COLOR
|
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Texture
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Light
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Medium
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Dark
|
|
Fine
|
4
|
20
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8
|
|
Medium
|
5
|
23
|
12
|
|
Coarse
|
21
|
23
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4
|
Illowsky - Ch. 11
True or False
5. 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 Table 11.55. Conduct a test for homogeneity at a 5% level of significance.
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French Toast
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Pancakes
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Waffles
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Omelettes
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Men
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47
|
35
|
28
|
53
|
|
Women
|
65
|
59
|
55
|
60
|
Use the following information to answer the next twelve exercises: 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.
6. df= _______
7. Let a = 0.05
Decision: _______
Conclusion (write out in a complete sentence): _________
The Regression Equation
8. Can a coefficient of determination be negative? Why or why not?
9. The cost of a leading liquid laundry detergent in different
sizes is given in Table 12.31.
|
Size (ounces)
|
Cost ($)
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Cost per ounce
|
|
16
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3.99
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|
|
32
|
4.99
|
|
|
64
|
5.99
|
|
|
100
|
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. Is the least-squares line valid for predicting what a 300-ounce size of the laundry detergent would you cost? Why or why not?
j. What is the slope of the least-squares (best-fit) line? Interpret the slope
Quiz 3
10. An assumption made about the value of a population parameter is called a
A. conclusion
B. confidence
C. significance
D. hypothesis
E. none of the above
11. The p-value is a probability that measures the support or lack of support for the
A. null hypothesis
B. alternative hypothesis
C. either the null or the alternative hypothesis
D. sample statistic
E. none of the above
12. In a t-test, which of the following does not need to be known in order to compute the p-value?
A. knowing whether the test is one-tail or two-tails
B. the value of the test statistic
C. the level of significance
D. the Degrees of Freedom
E. none of the above
13: As the test statistic becomes larger, the p-value
A. becomes smaller
B. becomes larger
C. becomes negative
D. stays the same because the sample size has not been changed
E. none of the above
14: What type of error occurs if you fail to reject H0 when, in fact, it is not true?
A. Type I
B. Type II
C. Either Type I or Type II, depending on the level of significance.
D. Either Type I or Type II, depending on whether the test is one tailed or two tailed.
E. None of the above.
15: The level of significance α is the
A. same as the p-value
B. 1 - β
C. maximum allowable probability of Type II error
D. maximum allowable probability of Type I error
E. none of the above
16: In hypotheses testing if the null hypothesis has been rejected when the alternative hypothesis is true, then
A. a Type I error has been committed
B. a Type II error has been committed
C. either a Type I or Type II error has been committed
D. the correct decision has been made
E. none of the above
17: In a one-tail, left-tail z-test, the test statistic is z = -2.01. The p-value is
A. 0.0179
B. 0.0228
C. 0.0222
D. 0.0174
E. none of the above
18: In a two-tail z-test, the test statistic is z = -2.5. The p-value for this test is
A. -1.25
B. 0.4938
C. 0.0062
D. 0.0124
E. none of the above
19: In a two-tail t-test, the test statistic t = -2.89 and the sample size is 30. The p-value is
A. 0.9928
B. 0.0019
C. 0.0038
D. 0.0036
E. 0.0072
20. In one-tail, left-tail t-test, the test statistic t = -1.58 and the sample size is 23. The p-value is
A. 0.0571
B. 0.9358
C. 0.0642
D. 0.1284
E. 0.0639
21: The average life expectancy of a certain brand of tire has been 40,000 miles. Because of a new manufacturing process
introduced it is believed that the life expectancy has increased. To test the validity of this the correct set of hypotheses is
A. H0: µ < 40,000 HA: µ ≥ 40,000
B. H0: µ = 40,000 HA: µ ≥ 40,000
C. H0: µ > 40,000 HA: µ ≤ 40,000
D. H0: µ = 40,000 HA: µ < 40,000
E. H0: µ = 40,000 HA: µ > 40,000
22: What kind of Alternative Hypothesis is used in the figure below?
A. HA: µ = µ0
B. HA: µ ≠ µ0
C. HA: µ > µ0
D. HA: µ < µ0
E. none of the above
23. Which type of Alternative Hypothesis is used in the figure below?
A. HA: µ = µ0
B. HA: µ ≠ µ0
C. HA: µ > µ0
D. HA: µ < µ0
E. none of the above
24: A soft drink filling machine, when in perfect adjustment, fills the bottles with 12 ounces of soft drink. If the machine
overfills or under fills then it must be shut down and readjusted. To determine whether or not the machine is properly
adjusted, the correct set of hypotheses is
A. H0: µ < 12 HA: µ ≥ 12
B. H0: µ = 12 HA: µ > 12
C. H0: µ ≠ 12 HA: µ = 12
D. H0: µ = 12 HA: µ ≠ 12
E. H0: µ = 12 HA: µ < 12
Use the following information to do the next four problems.
A random sample of 100 people was taken. In the sample 85% favored Candidate Green. We are interested in determining
whether or not the proportion of the population in favor of Green is significantly more than 80%.
25: The correct set of hypotheses for this problem is
A. H0: p = 0.85 and HA: p > 0.85
B. H0: p > 0.80 and HA: p = 0.80
C. H0: p = 0.80 and HA: p > 0.80
D. H0: p = 0.80 and HA: p ≥ 0.80
E. H0: p ≠ 0.80 and HA: p > 0.80
26: Find the test statistic.
A. 0.80
B. 0.05
C. 1.25
D. 2.00
E. none of the above
27: Find the p-value.
A. 0.1071
B. 0.8929
C. 0.8944
D. 0.1056
E. none of the above
28: At the 5% level of significance, can we conclude that the proportion of the population in favor of Green
A. is significantly greater than 80%
B. is not significantly greater than 80%
C. is significantly greater than 85%
D. is not significantly greater than 85%
E. none of the above
Use the following information to do the next four problems.
The sales of a grocery store had an average of $8,000 per day. The store started an aggressive advertizing campaign in order
to increase sales. To determine whether or not the advertizing campaign has been effective, i.e. the sales increased, a sample
of 66 days was selected. For this sample the mean was $8,300 per day and the standard deviation $1,200.
29: The correct Alternative Hypothesis for this problem is
A. HA: x‾ > 8,000
B. HA: x‾ ≥ 8,000
C. HA: µ > 8,300
D. HA: µ ≥ 8,000
E. HA: none of the above
30: The value of the test statistic is
A. -2.03
B. 2.03
C. -2.00
D. 2.00
E. none of the above
31: The p-value is
A. 0.0248
B. 0.0228
C. 0.9752
D. 0.9768
E. 0.0232
32: At the 5% level of significance, can we conclude that the advertizing campaign
A. increased sales?
B. decreased sales?
C. did not much affect sales?
D. was not worth the cost?
E. none of the above