Download All confidence intervals follow the same formula:

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.
S
Standard Error is found by
where S is the sample standard deviation and N is the
N
sample size. Completed, this looks like:
X  t*
S
N
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
the choices of degrees of freedom is minimal).
Substituting:
3.02  1.984 *
1.81
 3.02  1.984 * 0.081  3.02  0.161  2.859 to 3.181
497
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.