Basic Applied Statistics 200
Solutions to Practice Midterm 2

1.  
   1. correct: 9.50 is population mean, a parameter
   2. correct: 9.57 is sample mean, a statistic
   3. incorrect: 180 is sample size
   4. correct: no treatment has been imposed
   5. incorrect: sample mean is centered at 9.50
   6. correct: this is sigma divided by square root of sample size
   7. correct: from the Central Limit Theorem
2. 1. .40
   2. .40 + .30 = .70
   3. x-bar has mean 2.1, standard deviation 1.18/10 = .118
   4. P(x-bar < 2) = P(Z < -.85) = .1977
   5. 1. false: X is skewed right
      2. true
      3. false
      4. true : from the Central Limit Theorem
      5. true
3.  
   1. n = 12, p = .6
   2. mu = 7.2, sigma = 1.70
   3. (iii) No; 12 * .6 < 10, so our Rule of Thumb is not satisfied
4. 1. (23.71, 26.69)
   2. 1. lower
      2. less
      3. larger
   3. 35.7, so take n = 36
   4. (ii)
5.  
   1. null: mu = 22.6; alternative: mu > 22.6
   2. z = (25.2 - 22.6) / (6.1/(sq rt of 64))= 3.41
   3. P(Z > 3.41) = P(Z < -3.41) = .0003
   4. (i) small P-value means reject the null, conclude the alternative is true
6. 1. null: mu = 28.2; alternative: mu < 28.2
   2. t = (26.7 - 28.2)/(2.1/(sq rt of 9)) = -2.14
   3. 1.86 and 2.306
   4. .025 and .05
   5. Reject the null, because P-value < alpha
   6. Yes
   7. .05 and .10, so accept
   8. (i) and (ii) are true because 9 is a small sample size; sample mean isn't close to normal unless population is

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