For each of the following confidence intervals, indicate how much of the distribution would be placed in the cutoff region for a two-tailed test from 80%, 85% and 99%
80% = 10% at each end.
Generalize from this to the other two intervals.
To determine the cutoff region for a two-tailed test at different confidence levels, we need to calculate the proportion of the distribution that falls outside the confidence interval.
1. For an 80% confidence interval:
- The cutoff region for a two-tailed test in an 80% confidence interval would be (1 - 0.80) / 2 = 0.10 on each side of the distribution.
- Therefore, 10% of the distribution would be placed in the cutoff region for a two-tailed test from an 80% confidence interval.
2. For an 85% confidence interval:
- The cutoff region for a two-tailed test in an 85% confidence interval would be (1 - 0.85) / 2 = 0.075 on each side of the distribution.
- Therefore, 7.5% of the distribution would be placed in the cutoff region for a two-tailed test from an 85% confidence interval.
3. For a 99% confidence interval:
- The cutoff region for a two-tailed test in a 99% confidence interval would be (1 - 0.99) / 2 = 0.005 on each side of the distribution.
- Therefore, 0.5% of the distribution would be placed in the cutoff region for a two-tailed test from a 99% confidence interval.
In summary:
- For an 80% confidence interval, 10% of the distribution is in the cutoff region.
- For an 85% confidence interval, 7.5% of the distribution is in the cutoff region.
- For a 99% confidence interval, 0.5% of the distribution is in the cutoff region.
To determine the cutoff region for a given confidence interval in a two-tailed test, we need to consider the area or percentage of the distribution that falls outside the confidence interval.
1. 80% Confidence Interval:
For an 80% confidence interval, the cutoff regions for a two-tailed test would be (100% - 80%)/2 = 10% on each side. This means that 10% of the distribution would be placed in the cutoff region for both tails.
2. 85% Confidence Interval:
For an 85% confidence interval, the cutoff regions for a two-tailed test would be (100% - 85%)/2 = 7.5% on each side. This means that 7.5% of the distribution would be placed in the cutoff region for both tails.
3. 99% Confidence Interval:
For a 99% confidence interval, the cutoff regions for a two-tailed test would be (100% - 99%)/2 = 0.5% on each side. This means that 0.5% of the distribution would be placed in the cutoff region for both tails.
In summary, the percentage of the distribution that would be placed in the cutoff region for a two-tailed test from the given confidence intervals is:
- 80% confidence interval: 10% on each side
- 85% confidence interval: 7.5% on each side
- 99% confidence interval: 0.5% on each side