Basic Applied Statistics 200
Solutions to Midterm 2

1. (ii) is OK; not (i) because np = 7 < 10; not (iii) because n(1-p) = 4 < 10
2. 1. sample size n = 10 (200 is the population size)
   2. mean is np = 10(.7) = 7; standard deviation is square root of 10(.7)(1-.7), or 1.45
   3. (i) prevents binomial; non-random selection leads to dependence; (iii) has dependence because sample is more than 1/10 of population; (ii) is fine; don't confuse criteria for binomial setting with Rule of Thumb for approximating binomial with normal
3.  
   1. Probability in female circle, outside off-campus circle is .70 - .42 = .28; probability of overlap is .42; probability in off-campus circle, outside female circle is .60 - .42 = .18
   2. P(F or O)= .70 + .60 - .42 = .28 + .42 + .18 = .88
   3. P(O given F) = .42/.70 = .6
   4. independent because .7 * .6 = .42.
4. 1. mean = 38
   2. s.d. = 4.5 divided by square root of 900 = .15
   3. (iii) shape approximately normal because sample size is large
   4. (iii) 38.15 is not unusual---just 1 s.d. above the mean
5. Approximately 95% of the 100 intervals, or 95 intervals, should contain the population mean
6.  
   1. population size is 5000, sample size is 81, parameter is 7, statistic is 53
   2. 53 plus or minus 2.576 times 7 over square root of 81 = (51, 55)
   3. 1. lower confidence has smaller z* and a narrower interval
      2. higher stadard deviatin produces a wider interval
      3. larger sample size produces a narrower interval
   4. yes, reject the hypothesis that mean price is 50 because it is outside our interval
   5. ((1.645*7)/3)squared, or 14.75; round up to 15
7. 1. null hypothesis: mu = 2; alternative hypothesis: mu > 2
   2. t = (2.2-2)/(1.3/5)= .77 [ Note that SAMPLE s.d. was given.]
   3. Using 25 - 1 = 24 df in Table C, P-value is between .20 and .25
   4. (iv) P-value not small, so don't reject null hypothesis
   5.  
      1. Don't circle (i); population size 1000 is still more than 10 times sample size 25
      2. circle (ii); 25 is not a large enough sample to correct severe right skewness
      3. circle (iii); sample MUST be an SRS
8. 1. false; don't confuse statistical significance with practical significance
   2. true; very small P-value is very convincing evidence
   3. true; two-sided P-value is twice the one-sided P-value
9. (ii) large alpha is appropriate; if there's any doubt, we should reject the null hypothesis that the water is safe

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