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ConfidenceIntervals - the choices of degrees of freedom is...

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All confidence intervals follow the same formula: Sample Statistic +/- Multiplier*Standard Error For example in problem 7.25 on page 343 since we are talking about a 95% confidence interval to estimate a population mean the above formula would consist of: Sample Statistic is the sample mean X Multiplier would be a t-statistic from the t-table with degrees of freedom of N – 1. Standard Error is found by N S where S is the sample standard deviation and N is the sample size. Completed, this looks like: N S * t X ± Let us find the t multiplier and then substitute in values for the above formula. From the t-table (Appendix A Table B) and looking under the column of 95% for Confidence Level, we go to degrees of freedom closest to 497 – 1 = 496. We will use 100 giving us a multiplier of 1.984 (note that at this sample size the difference between the multipliers for
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Unformatted text preview: the choices of degrees of freedom is minimal). Substituting: = ± = × = ± 161 . 02 . 3 081 . * 984 . 1 02 . 3 497 81 . 1 * 984 . 1 02 . 3 859 . 2 to 3.181 Note that this differs slightly from that given in the book in part C but that is because we had to estimate our degrees of freedom from the table. Using a statistical program such as Minitab we would have arrived at the same answer as Minitab would have calculated a correct t multiplier for 496 degrees of freedom. In conclusion, we would say that we are 95% confident that the true mean number of children that females think is ideal is between 2.859 and 3.181 children. This exceeds the hypothesized value of 2 children leading us to believe that this hypothesized value is incorrect and is lower that expected....
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