Applied Statistical Methods 1000
Solutions to Practice Midterm 2

1. (b) [only one that has np and n(1-p) at least 10]
2. (a) and (b) [because population is normal] and (d) [because 40 is large enough to offset moderate skewness]
3.  
   1. (iii) because z=(750-592)/73=2.16
   2. (iii) because the scores are close to normal, so their normal probability plot is close to a straight line
4.  
   1. (iii) (large enough n ensures Central Limit Theorem applies
   2. (ii) (pop greater than 10n ensures dependence doesn't undermine formula for sd)
   3. PROPORTION has mean p=.2 and sd square root of p(1-p)/n = .05
   4. (i) because z=(.23-.20)/.05=.6 is not unusual
5.  
   1. mean of sample means is population mean 2, s.d. of sample means is population s.d. over square root of sample size, or .2
   2. (iii) As we take larger samples, the shape becomes closer to normal. However, 25 is a medium-sized sample, and the distribution is clearly right-skewed, so sample mean will still have right skewness.
   3. (iii) probabilities based on the normal curve aren't valid for skewed distributions
6.  
   1. (ii) (Small n yields smaller test statistic and larger p-value.)
   2. (i) (The null hypothesis is that the vaccine makes no difference.)
7.  
   1. 100(.05)=5
   2. 100(.95)=95
8.  
   1. Number with ADHD is .09(3000)=270. Interval is .48 plus or minus 2 times square root of .48(.52)/270=(.42, .54)
   2. (ii) because the interval straddles .5
   3. (i) because the multiplier would be less than 2
   4. (i)
9. 2 times square root of .49(.51)/1573=.025
10. (iii) This is a situation with a positive relationship (like heights and shoesizes) because fewer credits tend to go with less bookmoney and more credits with more bookmoney. Therefore, the sum of the two variables would tend more to the extremes: the variance of the sum is greater than the sum of the variances.
11.  
    1. (ii) (referring to t sketch, p-value>.05, so we can't reject Ho)
    2. (iii) (because standardized sample mean does not follow t distribution when sample is small and non-normal)
    3. (iii) (because sample is not representative)
    4. (i) (referring to z sketch because sample is large; p-value is just under .025, so we reject Ho
    5. (i) (it's the furthest AWAY FROM 600)
12.  
    1. (ii)
    2. (i) (p-value is only about half of the cut-off alpha=.05)
    3. .052 (twice the size)
    4. (iii) because the two-sided p-value is borderline
13. Extra Credit: the possible proportions are 0, .5, 1, with probabilities .25, .5, .25.

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