Basic Applied Statistics 200
Solutions to Practice Midterm 2

1.  
   1. (ii)
   2. (i)
   3. COUNT X has mean np=1600(.02)=32 and sd square root of np(1-p) = 5.6
   4. PROPORTION has mean p=.02 and sd square root of p(1-p)/n = .0035
   5. z=(.026-.02)/.0035=+1.71
   6. (iii) because z is somewhat unusual
2.  
   1. 52.5-3(2.5)=45
   2. z=(59-52.5)/2.5=+2.6
   3. (i) because z is greater than 2.576
3.  
   1. (ii)
   2. mean of sample means is population mean .4, s.d. of sample means is population s.d. over square root of sample size, or .1
   3. (ii) shape of distribution of sample mean is approximately normal because the sample size (64) is fairly large
   4. (i) because .7 is 3 standard deviations above the mean
4.  
   1. (ii)
   2. (i)
5.  
   1. (x)
   2. (iii)
6.  
   1. .65 plus or minus 2.326 times square root of (.65)(.35)/10=.65 plus or minus .11=(.54, .76)
   2. (ii)
   3. (i)
   4. (i)
   5. (ii)
7.  
   1. (ii)
   2. no (sample must be representative of the population)
   3. no (standardized sample mean only follows the t distribution if sample mean is approximately normal, which would not be the case if the distribution were skewed and the sample size were small)
   4. yes (sample mean is approximately normal if the sample is very large, even if the distribution is skewed)
   5. 2 (or 1.96) because the z distribution applies for large sample size
   6. (vi)
   7. Ho: mu=13.7, Ha: mu not equal to 13.7
   8. (i) because 13.7 is well-contained in the confidence interval
   9. (iii)
   10. (iii)
8.  
   1. (i)
   2. (iv)
   3. (i)
   4. (iii)
   5. (i)

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