(D) the Reduced Confidence Level Narrows the Width of the Confidence Interval

Estim8

 8 8.1 X  Z  = 85  1.96  , 83.04    86.96 n 64

 0.02 8.7 (a) X  Z   0.995  2.58 0.9877   1.0023 n 50 (b) Since the value of 1.0 is included in the interval, there is no reason to believe that the mean is different from 1.0 gallon. (c) No. Since  is known and n = 50, from the Central Limit Theorem, we may assume that the sampling distribution of X is approximately normal. (d) The reduced confidence level narrows the width of the confidence interval.  0.02 X  Z   0.995  1.96  0.9895   1.0005 n 50 (b) Since the value of 1.0 is still included in the interval, there is no reason to believe that the mean is different from 1.0 gallon.  0.05 8.9 (a) X  Z   1.99  1.96  1.9802   1.9998 n 100 (b) No. Since  is known and n = 100, from the central limit theorem, we may assume that the sampling distribution of X is approximately normal. (c) An individual value of 2.02 is only 0.60 standard deviation above the sample mean of 1.99. The confidence interval represents bounds on the estimate of the population average, not an individual value. (d) A shift of 0.02 units in the sample average shifts the confidence interval by the same distance without affecting the width of the resulting interval.  0.05 (a) X  Z   1.97  1.96  1.9602   1.9798 n 100

3.7417 8.13 Set 1: 4.5  2.3646 1.3719    7.6281 8 2.4495 Set 2: 4.5  2.3646 2.4522    6.5478 8 The data sets have different confidence interval widths because they have different values for the standard deviation. S 12.3868  8.19 (a) X  t  23.2  2.093  17.40    29.00 n  20  (b) You can be 95% confident that the mean amount of fat in the population of chicken sandwiches from fast-food chain is somewhere between 17.40 and 29.00 grams per serving. X 330 p(1– p ) 0.66(0.37) 8.27 (a) p = = = 0.66 p弊 Z = 0.66 1.96 n 500 n 500 0.62 ＃p 0.70 (b) You can be 95% confident that the population proportion of highly educated women who left careers for family reasons that want to return to work is between 0.62 and 0.70. Z 2 2 2.582 1002 8.35 n   = 166.41, Use n = 167 e2 202 p1 p 0.37991 0.3799 8.49 (a) p = 0.3799 p  Z  0.3799 1.96 n 658 0.3429 ＃p 0.4170 (b) You are 95% confident that the proportion of CEOs whose greatest concern was sustained and steady top-line growth in the population is somewhere between 0.3429 and 0.4170. Z 2 1   1.962 0.37991 0.3799 (c) n   = 9,049.92 Use n = 9,050 e2 0.012