Basic Applied Statistics 200
Solutions to Midterm 2

1.  
   1. 24+2(4)=32
   2. z=(17-24)/4=-1.75
   3. (iv) because z is between -1.96 and -1.645
2.  
   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. z=(.23-.20)/.05=.6
   5. (i) because z is not unusual
3.  
   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
4.  
   1. (ii) (Small n yields smaller test statistic and larger p-value.)
   2. (i) (The null hypothesis is that the vaccine makes no difference.)
5.  
   1. (ii)
   2. (vii)
6.  
   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
7.  
   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. (iii) (it's the furthest ABOVE 600)
   6. (i) (it's the furthest AWAY FROM 600)
8.  
   1. .63 plus or minus 2(.04)= (.55, .71)
   2. (i) because the multiplier would be less than 2
   3. (iii) because .75 is outside the interval
   4. (ii)
   5. (i)

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