1-Sample Z-Intervals

Worksheet 1 Solutions

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1. Solutions.
   1. The margin of error is 0.10. The CI is (35.18, 35.38).
   2. The procedure of forming 95% CIs has 95% reliability. That is, 95% of all samples result in an interval that covers the true (population) mean. So, you are 95% confident that the true mean is between 35.18 and 35.38.
   3. (35.12, 35.44)
   4. Higher confidence requires a larger margin of error.
   5. The margin of error is 0.20. The CI is (35.03, 35.43).
   6. When the sample size is increased by a factor of 4, the margin of error decreases by a factor of 2 (the square root of 4).
2. Solutions.
   1. The playing time of a CD Jill owns.
   2. All Jill's CDs (or the playing times of each of Jill's CDs).
   3. The mean playing time of all her CDs; the greek letter m is used for this.
   4. 47.927
   5. The margin of error is 2.87. The CI is (45.06, 50.80).
   6. The procedure of forming 90% CIs has 95% reliability. That is, 90% of all samples result in an interval that covers the true (population) mean. So, you are 90% confident that the mean playing time of all Jill's CDs is between 45.06 and 50.80 minutes.
   7. The type of music Jill listens to has a lower mean playing time than is the mean playing time of all CDs.