- The HIGHER the confidence interval is the WIDER it is and the more likely the population mean will fall within that range.
- Below is an example and my explanation of them:
- For some of the samples, the 75% confidence interval is included in the 90% confidence interval, while for other samples, this is not the case.
- This is NOT true. Both CI are based on the same samples, so ALL of the 75% CI would fit inside of the 90% CI
- We would expect to find more 90% confidence intervals that contain the population mean than 75% confidence intervals that contain the population mean. Given a sample, a higher confidence level results in a wider interval.
- This is TRUE. 90% is bigger than 87% so the 90% CI is wider and it will contain the population mean more often.
- It is surprising that some 75% confidence intervals are different from other 75% confidence intervals. They should all be the same, as long as the samples are random samples from the same population.
- This is NOT true. Every sample is different so of course you will have different numbers for each sample.
- Since Sample 19 and Sample 20 are drawn from the same population, the center of the 90% confidence interval for Sample 19 must be the same as the center of the 90% confidence interval for Sample 20.
- This is NOT true. They are drawn from the same population. BUT they are not the same SAMPLE. So they will not be the same.
- For some of the samples, the 75% confidence interval is included in the 90% confidence interval, while for other samples, this is not the case.