Basic Applied Statistics 200
Solutions to Practice Midterm 2

  1.  
    1. 130+3(20)=190
    2. P(X>160)=P(Z>(160-130)/20)=P(Z>+1.5)=P(Z<-1.5)=.0668
    3. Half of a normal variable's values fall below the mean: 130 [or take .5 is the probability of being below z=0 and unstandardize to 130+0(20)=130]
  2.  
    1. mean of sample means is population mean 7, s.d. of sample means is population s.d. over square root of sample size, or 1.67
    2. (iv) shape of distribution of sample mean is not necessarily normal because the sample size (5) is so small
  3.  
    1. (ii) binomial model
    2. (i) a normal approximation
    3. COUNT X has mean np=225(.10)=22.5 and sd square root of np(1-p) = 4.5
    4. P(X>37)=P(Z>(37-22.5)/4.5)=P(Z>3.22)=P(Z<-3.22)=.0006
    5. (ii) because of the small probability in (d)
    6. (iii) a parameter called p
  4.  
    1. 45/75=.6
    2. Ho:p=.25 vs. Ha:p>.25
    3. sd is square root of (.75*.25)/75 and z=(.60-.25)/sd=7
    4. P(Z>7)=0, approximately
    5. Since the p-value is extremely small, we reject Ho and conclude there is convincing evidence that the alternative is true: population proportion recovering with bat saliva treatment is significantly higher than usual (answer is (i) yes)
    6. Circle (ii) so subjects are blind, (iii) so there is a control group, and (v) so researchers are blind
  5.  
    1. 14.7 plus or minus 2.90(6)/3=(8.9, 20.5)
    2. (i) is the correct interpretation
    3. Ho: mu = 11.3 vs. Ha: mu > 11.3
    4. t=(14.7-11.3)/(6/square root of 9)=1.7
    5. For 8 df, 1.7 < 1.86 so P-value > .05 [Note: you must give a RANGE for the p-value for this and for part (f); it's important to know HOW the p-value compares to .05---whether it is smaller or larger.]
    6. (iv) the p-value is rather close to .05; more conclusive results may have been obtained from a larger sample [but I gave partial credit for (ii)]
    7. greater than 2(.05)=.10
  6.  
    1. In the long run, 99% of the 100 intervals, or 99, should contain p.
    2. In the long run, 1% of the 100 tests, or 1, should reject a true Ho.
    3. (iii) assume p=.5, p-value is probability of sample proportion less than or equal to .35
  7.  
    1. (ii) gives them more conviction
    2. (i) gives them more precision
    3. (iii) it depends
  8.  
    1. (ii) no, it was a two-sample study
    2. smaller n minus 1 = 10-1=9
    3. (i) we definitely reject the null hypothesis of equal times, because the p-value is close to zero
    4. (ii) maybe incorrect because of small samples
    5. (iii) one quantitative (times served) and one categorical (fraud or firearms)


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