Final answer:
To calculate the confidence interval for a population mean, you can use the formula (lower bound, upper bound) = (point estimate - EBM, point estimate + EBM), where EBM represents the margin of error. The degrees of freedom can be calculated by subtracting 1 from the sample size. The appropriate t value to use for a two-tailed 95 percent confidence interval can be found using a t-distribution table or calculator. The 95 percent confidence interval can then be calculated using the formula mentioned above. Similarly, the 99 percent confidence interval can be calculated using a different t value. If the sample size is different, the t value and resulting confidence interval will also change.
Step-by-step explanation:
The formula for calculating a confidence interval for a population mean, when the population standard deviation is unknown, is:
(lower bound, upper bound) = (point estimate - EBM, point estimate + EBM)
- To find the degrees of freedom (df), subtract 1 from the sample size (n). In this case, since the sample size is 20, the degrees of freedom would be 19.
- For a two-tailed 95 percent confidence interval, the appropriate t value to use in the formula is 2.093.
- To calculate the 95 percent confidence interval, you would use the formula mentioned above.
- To calculate the 99 percent confidence interval, you would use the same formula but with a different t value. For a two-tailed 99 percent confidence interval with 19 degrees of freedom, the t value is 2.861.
- If the sample size was 30 instead of 20, the 95 percent confidence interval can be calculated using the same formula, but the t value would be 2.042.