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Practice_Exam_I-CalcC

VIEWS: 4 PAGES: 11

									                                   Practice Exam I - Calculator
                                                        440/640
                                                  Experimental Methods
                                                      Spring, 2009

For calculation problems, start with the appropriate formula and show all the gory details.

   1)      Explain the role of inferential statistics in terms of samples and populations?




   2)      Which of the following is not the same sort of thing: {variance, median,
           range, standard deviation} and why?




   3)      Why do psychologists need to know statistics?




   4)      A study is conducted where a person’s average mood is measured as a
           function of body height. There are three happiness categories: happy, angry
           and sad. What is the independent variable? What is the dependent variable?
           What kind of scale is the independent variable on? What kind of scale is the
           dependent variable on?



   5)      Which is not a valid equation?
                n                         n            n
           a.    (X      i    Yi )   X i   Yi
                i1                       i1          i1
                 n
           b.   C    i    n *C
                i1
                 n                            n              n
     
           c.    (X      i    Yi )   X  Yi2
                                  2                2
                                                   i
                i1                        i1             i1
                      n               n
     
           d. C *  X i   C * X i
                      i1          i1

     

     
                                                                                             1
                 N            N
6)   Show that    (X i  C)   X i  NC
                 i1          i1




     


7)   Draw the histogram for this frequency distribution. What is the mode?



                  interval          frequency
                  10 to 19               5
                  20 to 29               8
                  30 to 39              13
                  40 to 49               3
                  50 to 59               7
                  60 to 69               2
                  70 to 80               1




8)   What is the sum of all the column heights in a relative frequency distribution?
     a. Infinity
     b. It depends on the probabilities
     c. 1
     d. 2.71828182845…
9)   What is the difference between a simple frequency distribution and a grouped
     frequency distribution?




                                                                                   2
10)   A group of third grade wrestlers have weights: 60, 60, 62, 62, 62, 65, 65, 66,
      67, 68, 69,70,70,71, and 83 pounds. Which wrestler(s) is (are) at the 75th
      percentile?




11)   In problem 8, what is the median?




12)   What is the relationship between the variance and the standard deviation?




13)   In a positively skewed distribution, which is likely to be larger?
      a. The mode
      b. The median
      c. The mean
      d. One is not likely to be larger than the other

14)   Calculate the biased standard deviation , for the data in problem 10. Start
      with the appropriate formula and show your calculation.




15)   What is the purpose of calculating a z score?



16)   Given the data in question 10, what are the
      a. Mean Z                        _____________
      b. Standard deviation of Zs      _____________
      c. Variance of Zs                _____________

17)   If resting heart rate is normally distributed in the population with μ = 72 and σ
      = 8, what is the percentile rank (approximately) of someone whose resting




                                                                                       3
       heart rate is 82?




 18)   What does the central limit theorem tell us?




 19)   All normal distributions can be described using the following equation:
                  1              2     2
       f (X)          e(X   ) / 2
                 2 2
           On the right hand side of the equation, which symbols are constants,
       which are variables and which are parameters? Hint: the parameters are those,
       which determine the location and width of the normal distribution.




 20)   What is the null hypothesis?




 21)   Which represents an area under part of the standard normal distribution curve?
       a. z
       b. 
       c. p
       d.  and p

 22)   Heart rates for a group of 25 joggers were measured, and the mean of the
       group was found to be 65 bpm. If the mean of the population is 72 bpm with
       a standard deviation of 10, what is the z-score for this group compared to
       other groups of the same size? Do Joggers have a significantly lower heart
       rate than the general population? Assume an  of .05.




                                                                                    4
23)   How does one get the sample distribution of the means from the distribution
      of the single scores?
      _______________________________________________________________
      _______________________________________________________________
      _______________________________________________________________
      _______________________________________________________________
24)   What is an alpha level?
      _______________________________________________________________
      _______________________________________________________________
      _______________________________________________________________
      _______________________________________________________________
25)   Explain the effects of alpha and N on type I and type II errors.
      _______________________________________________________________
      _______________________________________________________________
      _______________________________________________________________
      _______________________________________________________________
26)   A researcher tests a random sample of 25 college students to see how many
      hours they spend each day at the computer. The sample mean is 1.25 hours.
      If the population mean for this variable is .75 hours with a standard deviation
      of .4, what is the z-score for this group of college students (as compared to
      other groups the same size)?




27)   What is the relationship between the z distribution and the t distribution?
      How many t distributions are there? How many z distributions are there?
      _______________________________________________________________
      _______________________________________________________________
      _______________________________________________________________
      _______________________________________________________________
28)   When do we need to use the t-test instead of the z-test?
      _______________________________________________________________
      _______________________________________________________________
      _______________________________________________________________
      _______________________________________________________________

29)   When N is large we are more likely to accept our alternative hypothesis in a t
      test. There are two reasons for this. What are they? Hint: what is the effect
      of N on t and tcrit?
      _______________________________________________________________



                                                                                   5
      _______________________________________________________________
      _______________________________________________________________
      _______________________________________________________________
30)   Suppose you are computing a 95% confidence interval. What are you 95%
      confident of?
      _______________________________________________________________
      _______________________________________________________________
      _______________________________________________________________
      _______________________________________________________________


31)   Ace drug company is developing a new drug for depression. It is called
      Happyol. Pilot tests show that 20mg of Happyol works best on average. The
      standard deviation of optimal doses was 5mg in the same pilot tests.
      However, Ace needs to know how good of an estimate 20mg is with respect to
      the optimal dose for the entire population. Ace plans to conduct extended
      trials to prove that 20mg is 95% likely to be the true mean optimal dose, plus
      or minus 1.0 mg. How many patients do they need in their extended study?




32)   A group of students who agreed not to watch television for six months is
      asked how many books (other than those required for school) each read during
      that time period. The data are as follows: 7, 3, 8, 1, 2, 8, 4, 3, 0, 5. If the
      population mean for the number of nonrequired books read in six months by
      students the same age is 2.0, are the non-tv watchers exceptional?




33)   The marketing department of a manufacturing company wanted to find out
      how many blank video cassettes are purchased by the average American each
      year. The data for a random sample of Americans are as follows: 7, 0, 6, 3,
      10, 0, 4, 9, 6, 3, 12, 0, 5, 1, 8, 6. What are the limits of the 99% confidence
      interval for the mean of the population?




                                                                                        6
34)   In practice, the t test for two independent means is often more practical than
      the one sample t-test and the one sample z-test. Why is this?
      _______________________________________________________________
      _______________________________________________________________
      _______________________________________________________________
35)   When should the pooled variance t-test be used? When should the separate
      variance test be used?
      _______________________________________________________________
      _______________________________________________________________
      _______________________________________________________________
      _______________________________________________________________
      _______________________________________________________________

36)   Given the following data: X 1 = 8; X 2 = 5; s1 = 2; s2 = 3;N1 = 10; N2 = 15,
      what does the separate-variances t equal? Is the difference between means
      significant?




37)   Given the following data: 1 = 9; 2 = 6; s1 = 2; s2 = 1.5;N1 = 16; N2 = 21, what
      does the pooled-variances t equal? Is the difference between means
      significant?




                                                                                        7
38)   What is statistical power? How might having statistical power lead to
      misinterpreted results?
      _______________________________________________________________
      _______________________________________________________________
      _______________________________________________________________
      _______________________________________________________________

39)   Define type I and type II errors.
      _______________________________________________________________
      _______________________________________________________________
      _______________________________________________________________
      _______________________________________________________________


40)   What does it mean to say “an effect is significant?”




41)   In statistical power analysis, what do 1    ,  , and d represent? How are
      they affected by n, 1   2 , and  ?




42)   In an experiment that tests a single sample of 40 subjects against a
      hypothesized population mean, what would be your statistical power when
      dealing with an effect size d of .3 and performing an =.05 two tailed test?




43)   What is the purpose of linear correlation?




44)   When developing the formula for correlation, why do we map raw scores into
      z values?




                                                                                       8
45)   Suppose that 2 variables X and Y are closely related by the equation Y=X2.
      Is linear correlation a good tool for discovering such a relationship? Why?
      What about Y=aX+b?




46)   For the data below, what is the value of correlation coefficient r?

                                X              Y
                                5              4
                                6              3
                                8              6
                                9              6
                                4              4




47)   Given a correlation coefficient of -.52 from two variables measured on 14
      subjects, are the variables significantly correlated?




48)   What is the purpose of linear regression?




49)   In linear regression, the predicted value of Y, given X, is based on a weighted
      average of 2 distinct tendencies. What are they?


                                                                                    9
50)   To show that the number of hours spent studying can, to some degree, predict
      scores on a quiz, a professor collected the data presented below:

                                     Study         Quiz Score
                                     Hours
                                        7                5
                                        6               10
                                       11                6
                                        5                4
                                       15                9
                                       11               10
                                       12                8
                                       11                9
                                        7                7


      Determine the regression equation and predict the score of a student that
      studies 0 hours.

51)   Under which circumstances do you apply each test or analysis?
      a. One sample z-test
      b. One sample t-test
      c. Confidence interval of a mean
      d. z-test for two independent sample means
      e. t-test for two independent samples (separate variances)
      f. t-test for two independent samples (pooled variances)
      g. Linear correlation
      h. t-test of Pearson’s r
      i. Linear regression


52)   Extra credit: Prove that


                XY                  1
                                               XY  NXY 
                                      N 1
                             x   y
          r    N
                     x y                      sx sy



 



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