Basic Applied Statistics 200
Solutions to Midterm 2

1.  
   1. 4.1+2(0.1)=4.3
   2. z=(3.88-4.1)/0.1=-2.2
   3. (iii) because z is between -1.96 and -2.326
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=0.20
   4. z=(0.23-0.20)/0.05=+0.6
   5. (i) because z is not unusual
3.  
   1. mean of sample means is population mean 0.15; s.d. of sample means is population s.d. over square root of sample size, or 0.3
   2. (iii) As we take larger samples, the shape becomes closer to normal. However, 4 is a small-sized sample, and the distribution is clearly right-skewed, so sample mean will still have right skewness.
4.  
   1. (i) (They reject the null hypothesis that vaccines do not cause autism.)
   2. (ii) (The court did not reject the null hypothesis.)
5.  
   1. (iv) 0.10(150)=15
   2. (vii) 0.90(150)=135
6.  
   1. (ii)
   2. (iii) (P-value is slightly larger than 0.05, so if we use 0.05 as our cutoff, we can't quite reject)
   3. (iii) because the P-value is borderline
   4. 0.104 (twice the size)
7.  
   1. square root of 0.62(1-0.62)/1,042=0.015
   2. 0.68 plus or minus 2(0.015)= (0.59, 0.65)
   3. (i) because the multiplier would be less than 2 [not (ii): smaller n tends to give wider intervals]
   4. (iii) because 0.36 is way outside the interval
   5. (ii) [It's making a claim about p, not p-hat, but p does not obey the laws of probability, so we use the word "confidence".]
8.  
   1. (iii) (it's the farthest AWAY FROM 24)
   2. (i) (it's the farthest BELOW 24)
   3. (ii) (refer to t because n is small and sigma is unknown)
   4. (i) (refer to z because n is large; an outlier isn't a problem if n is large)
   5. (iii) (because sample is not representative)
   6. (iii) (because standardized sample mean does not follow t distribution when sample is small and non-normal)

[ Home | Calendar | Assignments | Handouts ]