STA 3024                                  EXAM 1 Practice Problems                        Fall 2006

 

NOTE:  These are just Practice Problems.  This is NOT meant to look just like the test, and it is NOT the only thing that you should study.  Make sure you know all the material from the notes, quizzes, suggested homework and the corresponding chapters in the book.

 

 

Questions 1 – 5  A poker craze seems to have swept the nation in the past couple of years, and some experts are concerned that it will lead to an increase in gambling addictions, particularly for adolescents.   Each of the five situations presented below describes an inference that we would like to make about a different parameter.  Match each of the five situations below with the parameter of interest from the list:

 

                                    a)  one mean

                                    b)  one proportion

c)  difference of two independent means

                                    d)  difference of two independent proportions

                                    e)  mean of matched paired differences

                                   

 

___  1.     A survey finds that 70% of children aged 12 to 17 have gambled in the past year.

 

 

___  2.     Although most children start playing just for fun, the average age at which they start gambling for money is around 11 years old.

 

 

___  3.     Among 8th graders, 42% of boys and 19% of girls gambled last year.

 

 

___  4.     Although some people claim that poker playing helps children with their math skills, a study found no increase in the average students’ math grades from before they started playing.

 

 

___  5.     Studies have found that boys bet higher amounts of money than girls, on average.

 

 

 

6.  An experiment was run to compare 8 groups.  There were 10 observations in each

    group.  How many degrees of freedom for error will there be? 

a)       2                     b)  9                 c)   73               d)  72                e)  76

 

 

7.  Find the value of the test statistic:                 

 a)  1.34                                                      Source      df           SS         MS           F

       b)  45.92                                                    Groups       5       

       c)  30.24                                                    Error                   453.6                          

       d)  1.52                                                      Total        20        683.2

 e)  0.66

 

8.  Use the F table to find the approximate p-value if  df numerator= 3, df denominator=5,

      and F= 14.72.  Our conclusions would be:

a)   reject Ho at 0.10 but not at 0.05                         b)  reject Ho at 0.05 but not at 0.025

c)   reject Ho at 0.025 but not at 0.01                        d)  reject Ho at 0.01 but not at 0.001

e)   reject Ho at 0.001

 

 

9.  Which of the following statements is true concerning the Mean Square Error:

a)         It is an estimate of the pooled variance for all the treatments.

b)         It can also be expressed as sp.

c)         It represents the variability between the treatments.

d)         All of the above.

e)         None of the above.

 

 

10.  When there are no significant differences in treatment means in ANOVA, we see:

a)      the variability within treatments is a lot smaller than the variability between

b)      the Sums of Squares for Error are very large

c)      the F test statistic is close to 1

d)      the p-value is very small

e)      all of the above

 

 

11.  What does the null hypothesis of the ANOVA test say?
a)  That the sample means for all treatments in the study are equal.

b)  That the population means for all treatments in the study are equal.
c)  That the sample means for all treatments in the study are different.
d)  That the population means for all treatments in the study are different.

e)  That the population mean for at least one of the treatments in the study is different from at

     least one other one.

 

 

12.  Below you will find a summary of the results of an experiment that fed rats different dietary supplements and measured their time to fall from a rotating rod.  Choose the best interpretation.

a)      All treatment means are significantly different, with blueberry best, then control, then strawberry, then spinach.

b)      Blueberry is significantly better than all the rest.

c)      Blueberry is significantly better, then strawberry and spinach (not significantly different from each other), and then control.

d)      Blueberry is significantly better, then control, and finally strawberry and spinach, which are not significantly different from each other.

 

 

Questions 13 - 19    Cereal leaf beetles can be very harmful to the cultivation of oats in the fields.  Researchers studied the effectiveness of traps constructed with bright, colorful boards, to attract the beetles.  The boards were covered with sticky material, so once the beetles landed on them, they were trapped.   To investigate which colors are most attractive to the beetles, six boards of each of four colors were randomly placed on oats fields.  The number of insects stuck to each board was counted and summarized below. 

Color                N         Mean                StDev 

Blue                        6              14.833                     5.345 

Green                      6              31.500                     9.915              

Yellow                    6              47.167                     6.795                           

White                     6              15.667                     3.327 

 

13.  The p-value of the ANOVA F test, according to Minitab, was 0.000.  We can conclude that there are significant differences in the average number of insects trapped on boards:

a)      for all the colors that were used in this study.

b)      for all the colors that could have been used in this study.

c)      for some of the colors that were used in this study.

d)      for some of the colors that could have been used in this study.

 

14.  To compare all pairs of means in this study, we would need to make six different confidence intervals.  If each individual confidence interval were made at the 95% confidence level, how much confidence would we have in the family of intervals?

a)      95%                 b)  94%                        c)  70%                        d)  89%                        e)  65%

 

15.  If we made all six pairwise confidence intervals with the Bonferroni procedure, using a family confidence of 94%, the value from the t table to use is:

a)      2.845                b)  3.708           c)  4.032           d)  5.841           e)  not on our table

 

16.  Which of the following would define the contrast to compare the effectiveness of the white board to the effectiveness of the other colors?

a)  μwhite – μblue –-μgreen– μyellow                            b)  μwhite – ½ μblue –- ½ μgreen– ½ μyellow

c)  μwhite – ⅓ (μblue +- μgreen+ μyellow)              d)  ¼ μwhite – ¼ μblue –- ¼ μgreen– ¼ μyellow

e)  none of the above

 

17.  Which of the following would define the contrast to determine if the yellow board is three times as effective as the white board?

a)  μwhite – μyellow                                                      b)  μwhite – 3 μyellow

c)  3 μwhite – μyellow                                                   d)  ⅓ μwhite –  ⅓ μyellow  

e)  none of the above

 

18.  The 95% CI for the contrast that compares the effectiveness of the yellow board vs the average of the blue and green boards is (16.92, 31.08).  We can conclude then, that:

a)      the yellow, blue and green boards are all significantly different in their effectiveness

b)      the yellow board is significantly more effective than the blue or green

c)      the blue and green boards are significantly more effective than the yellow

d)      the blue board is significantly more effective than the green

 

19.  Are there any problems with the assumptions of this test?

a)      Yes – the insects do not seem randomly drawn to all the colors, so there is a bias.

b)      Yes – we suspect the population standard deviations are not equal.

c)      Yes – both the randomness and equal variance assumptions seem to be violated.

d)      No – all the assumptions seem satisfied.

 

Questions 20 – 25   How do alcohol and sleep deprivation influence reaction time while driving?  Subjects were randomly assigned to drink a beverage containing either no alcohol or 1oz. of alcohol, and to conditions of either regular sleep or 24 hours of sleep deprivation.  Each group had the same number of subjects.  Using a driving simulation, they recorded each subject’s time (in milliseconds) to apply the car’s brakes after the sudden appearance of an unexpected object.  The average breaking time for each group, and the ANOVA table appear below.

 

 

 

 

 

Source

df

SS

MS

F

p

 

Sleep Deprivation

 

Alcohol

1

0.729

0.729

29.10 

0.000

 

Sleepdepriv

1

0.529

0.529

21.11 

0.000

Alcohol

none

24 hrs

 

Interaction

1

0.196

0.196

7.82 

0.008

0oz

0.68

0.81

 

Error

36

0.902

0.025

 

 

1oz

0.77

1.35

 

Total

39

2.356

 

 

 

 

20.  What are the treatments in this study?

a)      0oz alcohol, 1oz alcohol, no sleep deprivation, 24 hours sleep deprivation

b)      0.68, 0.77, 0.81, 1.35

c)      alcohol consumption, sleep deprivation

d)      alcohol, sleep deprivation, interaction, error

e)      0oz alcohol/no deprivation, 1oz alcohol/no deprivation,

0oz alcohol/24 hr deprivation, 1oz alcohol/24 hr deprivation,

 

21.  How many replications are there in this study?

a)  40                      b)  9                 c)  10                d)  36                e)  4

 

22.  What is the response variable in this study?

a)      alcohol consumption                   b)  sleep deprivation

c)    reaction time                            d)  milliseconds

 

23.  What type of study is this?

      a)  experiment                                 b)  observational study              

      c)  simulation                                   d)  survey

 

24.  A plot of the group means above will show:

a)      lines that cross each other         

b)      parallel lines

c)      non-parallel lines

d)      symmetric lines

e)      perpendicular lines

 

25.  Based on to the ANOVA table and the treatment means given above, which of the following is the best interpretation of the results?

a)      Both alcohol and sleep deprivation impair reaction time significantly.

b)      Alcohol and sleep deprivation impair reaction time, but not significantly.

c)      Both alcohol and sleep deprivation impair reaction time significantly, and their effects interact, creating an even greater impairment when combined.

d)      Alcohol and sleep deprivation impair reaction time, but their effects counteract each other, by lessening the impairment when combined.

e)      Neither alcohol, nor sleep deprivation, nor interaction, have a significant effect on reaction time.

 

26.  The error line on the ANOVA table represents:

a)      the possibility that the person making measurements made a mistake.

b)      the variability due to non-random error .

c)      all possible sources of variation that were not measured in the study.

d)      conscious efforts from the subjects to deviate from the means of their group.

 

27.  ANOVA is a statistical procedure used to compare the ___________ of different groups.

a)      means                      b)  variances          c)  sample sizes             d)  standard deviations

 

 

28.  In a study with 7 treatments, how many different pairwise comparisons would there be?

a)      7                             b)  6                      c)   21                           d)  42

 

 

29.  When making all pairwise comparisons in a study with equal sample sizes in all the four treatments, the margin of error was determined to be 7.00.  Which of the following could be the summary of the results?

a)

121.5 

b)

121.5

c)

121.5

d)

121.5

 

 

124.9

 

124.9

 

124.9

 

124.9

 

 

128.4

 

128.4

 

128.4

 

128.4

 

 

159.6

 

159.6

 

159.6

 

159.6

 

 

30.  Which of the following statements is True about comparisons using the Bonferroni method:

a)      It can only be used if the ANOVA null hypothesis is rejected.

b)      It can be used for pre-planned comparisons.

c)      It is necessary to adjust for the family confidence level desired.

d)      All of the statements above are true.

e)      None of the statements above are true.

 

31.  Which of the following statements is True about comparisons using contrasts:

a)      It can only be used if the ANOVA null hypothesis is rejected.

b)      It can be used for pre-planned comparisons.

c)      It is necessary to adjust for the family confidence level desired.

d)      All of the statements above are true.

e)      None of the statements above are true.

 

32.  Without replications we are unable to find:

a)  standard deviations for the groups                        b)  pooled standard deviation

c)  MSE                                                                  d)  F test statistic                      

e)  all of the above

 

33.  We use t** to make confidence intervals for:

a)  differences of two independent means                 b)  matched pairs differences    

c)  Bonferroni multiple comparisons                          d)  contrasts                 

e)  all of the above

 

34.  In ANOVA, which of the following would result in a more complicated statistical analysis?

a)  adding 500 more observations                              b)  adding 25 more levels of a factor

c)  adding one more factor                                       d)  adding 10 more replications

 

 

ANSWERS

 

  1. b
  2. a
  3. d
  4. e
  5. c
  6. d
  7. d
  8. d
  9. a
  10. c
  11. b
  12. b
  13. c
  14. c
  15. a
  16. c
  17. e
  18. b
  19. b
  20. e
  21. c
  22. c
  23. a
  24. c
  25. c
  26. c
  27. a
  28. c
  29. b
  30. d
  31. b
  32. e
  33. c
  34. c