Review Part 2 by HC120718072846

VIEWS: 38 PAGES: 18

									                         Review Questions
1. A student wonders if people of similar heights tend to date each other. She
measures herself, her dormitory roommate, and the women in the adjoining rooms;
then she measures the next man whom each woman dates. Here are the data (heights in inches):

Women      64          65          65          66         66           70
Men        68          68          69          70         72           74

Determine whether each of the following statements is true or false.

a)     If we had measured the heights of the men and women in centimeters (1 inch  2.5 cm), the
correlation coefficient would have been 2.5 times larger.

b) There is a strong negative association between the heights of men and women because the women
are always smaller than the men they date.

c) There is a positive association between the heights of men and women.

d) Any height above 70 inches must be considered an outlier.
             Review Questions

2. Determine whether each of the following
   statements regarding the
correlation coefficient is true or false.


a) If r is the correlation between X and Y, then –r is
   the correlation between Y and X.

b) If r is the correlation between X and Y, then 2r is
  the correlation between 2X and Y.
                 Review Questions
3. In a statistics course, a linear regression equation was computed to
predict the final exam score from the score on the midterm exam. The
equation of the least-squares regression line was y = 10 + 0.9x,
where y represents the final exam score and x is the midterm exam
score. Suppose Joe scores a 90 on the midterm exam. What would be
    the predicted value of his score on the final exam?

A) 81           B) 89           C) 91

D) Cannot be determined from the information given. We also need to
   know the correlation.
             Review Questions
4. In a study of 1991 model cars, a researcher computed
   the least
squares regression line of price (in dollars) on
   horsepower. He
obtained the following equation for this line price = –
   6677 + 175 ×
horsepower. Based on the least-squares regression line,
   what would
we predict the cost of a 1991 model car with horsepower
   equal to 200
to be?

A) $41,677 B) $28,323          C)$35,000    D)$13,354
                    Review Questions
5. The correlation coefficient between two variables X and Y is r = 0.121.
    What conclusion can we draw?

a)   Because the correlation is so low, the relationship between X and Y is not
     very strong, thus there is no use in studying this relationship.

b) Because the correlation is so low, we only know that the linear relationship
    between X and Y is not very strong, but there may a different relationship
    between the two variables. We need to first look at a scatterplot.

c) The correlation between X and Y is low, but that does not matter. We can
    still use least-squares regression to calculate an equation of the form = ax
    + b.

d) None of the above.
Use the following to answer questions 6-8: A market research company employs a large
   number of typists to enter data into a computer data base. The time it takes for
   potential new typists to learn the computer system is known to have a normal
   distribution with a mean of 90 minutes and a standard deviation of 18 minutes. A
   candidate is automatically hired if she learns the computer system in less than 100
   minutes. A cut-off time is set at the slowest 10% of the learning distribution. Anyone
   slower than this cut-off time is definitely not hired.


6) What proportion of candidates takes more than two hours to learn the computer
    system?
• A)0.048                   B)0.452            C)0.711             D)0.952



7) What proportion of candidates will be automatically hired?
• A)0.048                     B)0.452            C)0.711             D)0.952
• Answer:
•
8) What is the cut-off time the market research company uses?

A)1 hour and 7 minutes.                B)1 hour and 53 minutes.
C)2 hours.                                       D)2 hours and 8 minutes.
Determine whether each of the following statements is true or false.

9. The margin of error for a 95% confidence interval for the mean m
    increases as the sample size increases.

10. The margin of error for a confidence interval for the mean m,
   based on a specified sample size n, increases as the confidence
   level decreases.

11. The margin of error for a 95% confidence interval for the mean m
   decreases as the population standard deviation decreases.

12. The sample size required to obtain a confidence interval of
   specified margin of error m, increases as the confidence level
   increases.
• Answer:
Use the following to answer questions 13 and 14: The heights of
   a simple random sample of 400 male high school sophomores
   in a Midwestern state are measured. The sample mean is
   66.2 inches. Suppose that the heights of male high school
   sophomores follow a normal distribution with standard
   deviation s = 4.1 inches.
13. What is a 95% confidence interval for m?
A) (58.16, 74.24)                   B)(59.46, 72.94)

C) (65.80, 66.60)                   D)(65.86, 66.54)
14. Suppose the heights of a simple random sample of 100 male
sophomores were measured rather than 400. Which of the
Following statements is true?
A) The margin of error for the 95% confidence interval would
   increase.

B) The margin of error for the 95% confidence interval would
   decrease.

C) The margin of error for the 95% confidence interval would
   stay the same, because the level of confidence has not
   changed.
D) The standard deviation s would decrease.
15. The scores on the Wechsler Intelligence Scale
for Children (WISC) are thought to be normally
distributed with standard deviation s = 10. A simple
random sample of 25 children is taken, and each is
given the WISC. The mean of the 25 scores is =
104.32. Based on these data, what is a 95%
  confidence
interval for m?

A) 104.32 ± 0.78       B) 104.32 ± 3.29

C) 104.32 ± 3.92       D) 104.32 ± 19.60
Use the following to answer questions 16 and 17: Battery packs
in radio-controlled racing cars need to be able to last pretty long.
The distribution of the lifetimes of battery packs made by Lectric
Co. is slightly left skewed. Assume that the standard deviation of
the lifetime distribution is s = 2.5 hours. A simple random sample
of 75 battery packs results in a mean = 29.6 hours.

16. What is a 90% confidence interval for m, the true average
lifetime of the battery packs made by Lectric Co.?

A) (29.13, 30.07)              B)(29.03, 30.17)

C)(28.86, 30.34)              D) The confidence interval cannot
   be calculated, because the population distribution is not
   normal.
•
•
17. Determine whether each of the following statements is true or false.
A) If a 95% confidence interval had been calculated, the margin
of error would have been larger.

B) If many more samples of 75 battery packs were taken, 90% of the resulting
    confidence intervals would have a sample mean between 29.13 and 30.07.

C) If the sample size had been 150 and not 75, the margin of error would have
    been larger.
18. Scores on the SAT Mathematics test are
believed to be normally distributed. The scores of a
simple random sample of five students who
recently took the exam are 550, 620, 710, 520, and
480.What is a 95% confidence interval for m, the
481.population mean score on the SAT Math test?

A) (456.7, 695.3)            B) (463.4, 688.6)

C) (480.8, 671.2)            D) (496.5, 655.5)
Use the following to answer questions 21-24: Bags of a certain brand of tortilla chips claim to have a net weight
of 14 oz. Net weights actually vary slightly from bag to bag. Assume net weights are normally distributed. A
representative of a consumer advocate group wishes to see if there is any evidence that the mean net weight is
less than advertised and so intends to test the hypotheses H0: m = 14, Ha: m < 14. To do this, he selects 16 bags
of tortilla chips of this brand at random and determines the net weight of each. He finds a sample mean of
13.88 oz. with a standard deviation of s = 0.24 oz.

19. What is the value of the test statistic?
•    A) t = –0.50         B) t = –2.00                C) t = –8.00                        D) t = –8.33
•    Answer:



20. Determine which of the following statements regarding the decision the representative would make is true.

A) He would not reject H0 at a significance level of 0.05.

B) He would reject H0 at a significance level 0.05, but not at 0.025.

C) He would reject H0 at a significance level 0.025, but not at 0.01.

D) He would reject H0 at a significance level 0.01.
•   Answer:
•   Use the following to answer questions 24-26: After once again losing a football game to the college’s arch
    rival, the alumni association conducted a survey to see if alumni were in favor of firing the coach. A simple
    random sample of 100 alumni from the population of all living alumni was taken. Sixty-four of the alumni
    in the sample were in favor of firing the coach. Let p represent the proportion of all living alumni who
    favor firing the coach.

•   21. What is a 99% confidence interval for p?
•   A) 0.64 ± 0.048                  B)0.64 ± 0.079                          C)0.64 ± 0.094
•   D) 0.64 ± 0.124
•   Answer:




•   22. Suppose the alumni association wished to see if the majority of alumni are in favor of firing the coach.
    To do this they test the hypotheses H0: p = 0.50 versus Ha: p > 0.50. What is the P-value for this hypothesis
    test?
•   A) below 0.001
•   B) 0.0026
•   C) 0.0682
•   D) 0.14

•
• 23. Suppose the alumni association wished to
  conduct the test at a 5% significance level.
  What would their decision be? Based on that
  decision, what type of mistake could they
  have made?
A) Accept H0, Type I error
B) Accept H0, Type II error
C) Reject H0, Type I error
D)Reject H0, Type II error
                 Answer Key
1. A) False, B) False, C) True, D) False
2. A) False, B) False
3. C
4. C
5. B
6. A
7. C
8. B
9. False
10.False          11) True,         12) True
•   13. C
•   14. A
•   15. C
•   16. A
•   17. A) True, B) False, C) False, D) True
•   18. B
•   19. B           20. B       21. D       22. B
•   23. C

								
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