Confidence Interval (Women’s Heights)
Confidence Interval (Women’s Heights)
Class Time:
Names:
Student Learning Outcomes
- The student will calculate a 90% confidence interval using the given data.
- The student will determine the relationship between the confidence level and the percentage of constructed intervals that contain the population mean.
Given:
| 59.4 | 71.6 | 69.3 | 65.0 | 62.9 | 66.5 | 61.7 | 55.2 |
| 67.5 | 67.2 | 63.8 | 62.9 | 63.0 | 63.9 | 68.7 | 65.5 |
| 61.9 | 69.6 | 58.7 | 63.4 | 61.8 | 60.6 | 69.8 | 60.0 |
| 64.9 | 66.1 | 66.8 | 60.6 | 65.6 | 63.8 | 61.3 | 59.2 |
| 64.1 | 59.3 | 64.9 | 62.4 | 63.5 | 60.9 | 63.3 | 66.3 |
| 61.5 | 64.3 | 62.9 | 60.6 | 63.8 | 58.8 | 64.9 | 65.7 |
| 62.5 | 70.9 | 62.9 | 63.1 | 62.2 | 58.7 | 64.7 | 66.0 |
| 60.5 | 64.7 | 65.4 | 60.2 | 65.0 | 64.1 | 61.1 | 65.3 |
| 64.6 | 59.2 | 61.4 | 62.0 | 63.5 | 61.4 | 65.5 | 62.3 |
| 65.5 | 64.7 | 58.8 | 66.1 | 64.9 | 66.9 | 57.9 | 69.8 |
| 58.5 | 63.4 | 69.2 | 65.9 | 62.2 | 60.0 | 58.1 | 62.5 |
| 62.4 | 59.1 | 66.4 | 61.2 | 60.4 | 58.7 | 66.7 | 67.5 |
| 63.2 | 56.6 | 67.7 | 62.5 |
- (Figure) lists the heights of 100 women. Use a random number generator to select ten data values randomly.
- Calculate the sample mean and the sample standard deviation. Assume that the population standard deviation is known to be 3.3 inches. With these values, construct a 90% confidence interval for your sample of ten values. Write the confidence interval you obtained in the first space of (Figure).
- Now write your confidence interval on the board. As others in the class write their confidence intervals on the board, copy them into (Figure).
90% Confidence Intervals __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________
Discussion Questions
- The actual population mean for the 100 heights given (Figure) is μ = 63.4. Using the class listing of confidence intervals, count how many of them contain the population mean μ; i.e., for how many intervals does the value of μ lie between the endpoints of the confidence interval?
- Divide this number by the total number of confidence intervals generated by the class to determine the percent of confidence intervals that contains the mean μ. Write this percent here: _____________.
- Is the percent of confidence intervals that contain the population mean μ close to 90%?
- Suppose we had generated 100 confidence intervals. What do you think would happen to the percent of confidence intervals that contained the population mean?
- When we construct a 90% confidence interval, we say that we are 90% confident that the true population mean lies within the confidence interv