Statistics in a Modern World 800
Solutions to Practice Exam 4

  1.  
    1. mean of sample proportions is population proportion .5
    2. standard error is square root of (.5(1-.5)/25) = .1
    3. shape is normal or bell-shaped
    4. 68% within .1 of .5: between .4 and .6
    5. 95% within 2(.1) of .5: between .3 and .7
    6. 99.7% within 3(.1) of .5: between .2 and .8
  2. (c) (-.5, 2), because this interval contains zero
  3. (a) (5,8) and (6,9) have the most overlap
  4. (b) (5,8) and (9,12) are furthest from each other
  5.  
    1. 57 plus or minus 2(3)/10 = 57 plus or minus .6 = (56.4, 57.6)
    2. (i) wider because square root of sample size is in the denominator of the margin of error
    3. (iii) unreliable because the sample is not random
    4. (i) 90% refers to chance of success of the method
  6. (c) .0549 could be considered a borderline p-value; a larger sample may yield more conclusive results
  7. (c) the sample must be random, and there should be at least 5 of each type of outcome: here there'd be about 8 in the category of interest, 72 not
  8.  
    1. (ii) null hypothesis states population proportion = .5
    2. (iii) alternative hypothesis states population proportion > .5
    3. (i) hypothesized population proportion is used to calculate standard error
    4. square root of (.5(1-.5)/49) = .07
    5. z = (.63 - .50)/.07 = 1.86
    6. p-value = probability of z > 1.86 = probability of z < -1.86 = .03
    7. yes, there is convincing evidence that a majority prefer fresh-brewed
  9. (a) is matched pairs because 2 measurements are made on the same individuals
  10. p-value for two-sided test is 2(.03) = .06
  11. (a)very small p-value means strong evidence of a difference; it doesn't necessarily mean the difference is large
  12. (b) Simpson's paradox means a change in the relationship in a two-way table when tables are combined, so the survival rate would be higher in hospital B

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