STAT 160
FINAL REVIEW
 
 

1) In a tasting test among three beverages A, B and C,  the following proportions of the sample opted for a particular beverage. What is  the best conclusion:

        A            B            C
        38%        32%        30%

(a) A is preferred in general population
(b) C is a less popular drink
(c) the population's choice is equally divided among the three
(d) more informaton is needed in order to reach a conclusion
 

2)  In a factory , an engineer wanted to see what effect two processes X and Y had on the productivity. In the first week they used process X, and in the second week they used process Y. Assume that a 95 % CI of difference in productivity (Y -X) is ( -7.5 ; 69.91). What does this mean in terms of the problem?

(a) Process Y is better
(b) Processes are approximately the same
(c) We cannot say which is better, but X and Y are different
(d) Process X is better
 

3) A new treatment is tested in a clinic. Out of 80 patients, 56 were cured. Find a 95% CI for the cure rate.

(a) (.517 ; .883)
(b) (.579 ; .820)
(c) (.599 ; .800)
(d) (.547 ; .853)
 

4) Use the following stem and leaf plot to determine the shape of the distribution:

    The decimal point is at the |

    -1|43
    -0|8865
     0|2345679
     1|112446778
     2|0778
     3|589
     4|16
     5|8
     6|03
     7|0

    (a) left skewed
    (b) symmetric
    (c) right skewed
 

5) Find the outliers for the following data set:

        12  98  21  24  59   28  29  26  9  38   33  11  47

    (a) 59, 98
    (b) 47
    (c) no outliers
    (d) 98
 

Problems 6 - 8:

    Four bowling balls were randomly selected and then each was weighed using two different scales: Scale 1 and Scale 2.  The results are:

                Ball 1        Ball 2        Ball 3        Ball 4
Scale 1      6.5            6.6            12.6          10.8
Scale 2      9.4            9.4            11             11
 

6) What type of design is this:

(a) regression
(b) completely randomized
(c) paired
(d) covariate
 

7) Let Delta be the true effect of Scale 2 - Scale 1. For testing this effect,  find the value of the Wilcoxon test statistic for this problem.

(a) 9
(b) 10
(c) 8
(d) 5
 

8) Find the Hodges-Lehmann estimate of Delta , the true effect of Scale 2 - Scale 1

(a) 2.05
(b) -2.05
(c) 2.3
(d) 1.075
 

Problems 9, 10 :

    Given the scatterplot :
 


 

9)  What is the relationship between X and Y :

(a) no relationship between them
(b) as X increases, Y decreases
(c) as X increases, Y increases
(d) as X increases, Y stays the same
 

10) Guess the correlation coefficient

(a) 1
(b) .8
(c) -.8
(d) -1
 

11) For the presidential elections in a school, out of 20 students in the first class, 10 voted for Candidate A (50% favored him) and out of 30 students in the second class, 18 voted for the same candidate (he was favored by 60% of these students). Using the following output, can you conclude that there is a difference between the two classes in the percentage of students favoring this candidate?


 

(a) No, the results are inconclusive
(b) The second class seem to like the candidate better
(c) The first class seem to like the candidate less
(d) Candidate A will get elected, anyway
 

12) From a deck of 52 cards (26 red cards and 26 black cards), 3 cards are drawn without replacement.
      What is the probability of getting a red or black card in the first drawing?

    (a) .5
    (b) 0
    (c) 1
    (d) .25
 

Problems 13 , 14 :

    The usual success rate of a particular missile is 80%. If 12 missiles are fired independently of one another, find the probability that exactly 10 are successful.
     Consider the following resampling model to determine this probability. Select 12 single digit random numbers from 0, 1, ..., 9 with replacement. Let number 1 - 8 represent success and numbers 0 and 9 represent failure. Use the results of 10 trials of this resampling model given below:

13) What type of sampling is appropriate:

(a) we cannot tell
(b) with replacement
(c) both (b) and (d)
(d) without replacement
 

14) Determine the estimate of the probability based on these trials:

(a) 0
(b) .1
(c) .7
(d) .3
 

Problems 15, 16:

              Assuming the LS fit for a regression analysis is : Y = 747.2 - 4.12 X

15) What does the estimate of the slope mean?

(a) as X increases by 1 unit, Y increases by 747.2 units
(b) as X increases by 1 unit, Y decreases by 4.12 units
(c) as X increases by 1 unit, Y increases by 4.12 units
(d) as Y increases by 1 unit, X decreases by 4.12 units
 

16) Find the predicted value and the residual for X = 23, if the observed Y value for X = 23 is  Y = 652.

(a) predicted = 17090.84 ; residual = -16438.84
(b) predicted = 652.44 ; residual = -.44
(c) predicted = 652.44; residual = 652
(d) predicted = 652 ; residual = 23
 

17)  Consider the following situation: Clinical trials have shown that 80% of the patients with migraines experience relief from their pain after using a specific new drug. If 16 migraine patients try the drug , and you are interested in the probability that all of them experience relief, how do you set up a Binomial model?

(a) n = 16 ; p = .2 ; k = 16
(b) n =16 ; p = .8 ; k = 16
(c) n = 16 ; lambda = .8
(d) n = 100 ; p = .8; k = 16
 

18) On a multiple-choice quiz, Joan guesses on each of five questions. Each question has 4 choices, only one of which is correct. What is the probability that Joan gets less than 3 right (no more than 2)? (use one of the following three binomial probability outputs from the Probability module)
 
 
n = 5 
p = .25
P(X = 3) = .0879
P(X <= 3) = .9844
n = 5
p = .25
P(X = 2) = .2637
P(X <= 2) = .8965
n = 5
p = .3
P(X = 4) = .0284
P(X <= 4) = .9976

(a) .896
(b) .264
(c) .088
(d) .104
 
 

Problems 19 - 21 :

         A certain chemical is produced by cooking it in a large pressurized vat.   To investigate the effect of pressure on yield, an experiment was conducted at 8 different levels of pressure. At each level, the yield of the chemical was recorded.  For the experiment, all other factors that could affect yield were kept constant.

Pressure (X):   2    4     6     8    10    12    14    16
Yield (Y):        8    9   15   19    23    24    20    16
 

19)  Scatterplot this data, Yield versus Pressure.   What is the most appropriate description of the plot:

(a) Increasing trend which is exponential.
(b) Increasing trend which is linear.
(c) Increasing trend but there is a downward curve at the end.
(d) There is no relationship between X and Y.
 

20)  Regardless to your answer of (19), a linear model was fit to this data, i.e.

         Yield = a + b*Pressure + Error

    Assume this model is correct.
    Below is selected output from the regression module.  Use the Wilcoxon analysis to determine a 95% confidence interval for b.  Then determine the correct decision  of the test
       H0:  b = 0     versus      HA: b not equal to 0
 
 
 
Least Squares Analysis

Coefficients: 
            Estimate Std. Error t value 
(Intercept)   9.1429     3.5916   2.546 
X             0.8452     0.3556   2.377 
 

Wilcoxon Analysis

                  Coef   Std. Err   t-ratio 
intercept   7.5   6.420060   1.16821 
X           1.0   0.622102   1.60745 


 

(a) (-.219, 2.219) Yield is not linearly related to pressure.
(b) (.383, 1.717) Yield is not linearly related to pressure.
(c)  (.148, 1.542) Yield is linearly related to pressure.
(d) (.378, 1.622) Yield is linearly related to pressure.
 

21) What type of design is this?

(a) Randomly paired design.
(b) Completely randomized design.
(c) Controlled regression design.
(d) An uncontrolled regression design.
 

Problems 22, 23:

     Given the data set :

      8   9  12   15

22)  Find the sample mean and standard deviation of this data set:

(a) mean =11.5 ; stdev = 3.162
(b) mean = 11 ; stdev = 9.998
(c) mean = 11 ; stdev = 2.739
(d)  mean = 11 ; stdev = 3.162
 

23)  Obtain a 95% Confidence Interval for mu:

(a) (4.802 ; 17.198)
(b) (7.901 ; 14.099)
(c) (5.632 ; 16.368)
(d) (8.261 ; 13.739)
 

24)  The heights of 10-year-old boys are believed to follow the normal distribution with a mean of 64 inches and a standard deviation of 4. How tall is a boy if  25 % of boys are shorter than he is ? (use Probability module output)
 
 
 
mu = 0
Std. Dev. = 1
P(Z < -0.674) = .25
mu = 0
Std. Dev. = 1
P(Z < 0.674) = .75

 

(a) 66.696
(b) 65
(c) 61.304
(d) 67
 

25) A set of 64 independent measurements of the length of a microorganism is made.  The true mean value and the true standard deviation of such a measurement are 27.5 and 3.2, respectively. Find the probability that the average microorganism has a length of  less than 27 micrometers. (use Probability module output)
 
 
mu = 27.5
Std. Dev. = 3.2
P(Z < 27) = .438
mu = 27.5
Std. Dev. = 0.4
P(Z < 27) = .106
mu = 27
Std. Dev. = 0.4
P(Z < 27.5) = .894

 
 

(a) .894
(b) .106
(c) .438
(d) .562
 

26)  A sample is given by

                    12   34   46   48   49   50   50   67   79   81   98   102

    The resampling code obtained the medians of 100 resamples, which are given below.
    Find the 95% confidence interval for the population median:

(a) (30 ; 100)
(b) (31 ; 91.5)
(c) (29 ; 100)
(d) (39.5 ; 89.5)
 

27) 8 patients were randomly chosen and then randomly split into two groups of 4 in order to test the effectiveness of a new drug as compared to a standard one. What type of design is this:

(a) Randomly paired design
(b) Observational Design
(c) Completely randomized design
(d) Controlled regression design
 

Problems 28 - 30 :

        There are two species of rats that live in a certain area.  The one species, Type A, are thought to weigh more than Type B.   Two samples produced the results given below. Suppose we want to test this alternative hypothesis using the Wilcoxon statistic, T = number of positive differences (Type A - Type B)

    Type A        67    53   68
    Type B        35    60   72    20  80   15

28) What do we expect T to be if the weights of typical rats from these two species are the same.

(a) 18
(b) 9
(c) 6
(d) 12
 

29)  Compute the value of the statistic T:

(a)12
(b)11
(c) 9
(d) 10
 

30) Suppose we commit a Type I error when we test this hypothesis. What does this mean?

(a) We conclude that Type A rats weigh less than Type B when they really weigh more
(b) We conclude that Type A rats weigh the same as Type B when they really weigh more.
(c) We conclude that Type A rats are heavier than Type B when they really are not.
(d) It is impossible to tell.
 

Problems 31 - 34 :

     We have 2 groups of patients in a drug study for lowering cholesterol: Old Drug  and New Drug . It is thought that the new drug is better than the old (where better means smaller values, here).

        Old Drug       47      68        79     116
        New Drug     30      34        59     125

31)  Let T be the number of differences (Old Drug - New Drug) which are positive. A quick calculation gives T = 11.   Compute the p-value based on the 100 resamples:

(a) .20
(b) .19
(c) .165
(d) .81
 

32)  What is the conclusion using a level of significance of .05:

(a) Drug Y is better
(b) There is no difference between the two drugs
(c) Drug X is better
(d) Sample sizes are too small
 

33)  Suppose the p-value came out to .001.  A 95% confidence interval, based on the Wilcoxon, for the effect (Old - New) would contain  :

(a) The value 0
(b) All negative values
(c) A mixture of negative and positive values
(d) All positive values
 

34) If the last data point for the New Drug was changed to 1250, would the value of the test statistic change?

(a) Can't say
(b) Yes
(c) No
(d) Depends on the day of the week
 

35) Polls of wealthy financial bankers before and after president Jane Smith  made a controversial decision were tabulated and given to her. Find a point estimate of the difference in proportions of contributing bankers.

                      Will Contribute   Will Not
     Before Decision        72            30
     After Decision         68              92

(a) .28
(b) .04
(c) 4
(d) .62