Final answer:
The 94% confidence interval of (–32 hours, 5 hours) for the difference in paid leave suggests there may be no difference or that Group A might have less leave than Group B, but it includes the possibility of no difference.
Step-by-step explanation:
When a 94% confidence interval for the mean difference in the annual amount of paid leave between Group A and Group B is calculated to be (–32 hours, 5 hours), it suggests that we are 94% confident that the true mean difference lies within this range. If Group A is having negative values as part of its interval, it could mean that Group A potentially has less annual paid leave compared to Group B. However, since the interval includes 0, it is also plausible that there is no difference in the amount of paid leave between the two groups.
Using a plus-four method to calculate a 97 percent confidence interval for the population proportion, takes into account the sample proportion and adds four to both the number of successes and the number of trials. This adjusts the interval for small sample sizes or proportions close to 0 or 1, aiding in creating a more precise estimate of the true population proportion.
The width of the confidence interval is affected by the level of confidence: a higher confidence level will result in a wider interval, as seen in the provided study, which exemplifies the principles of normal distribution and error bounds in constructing confidence intervals.
If a confidence level decreases from 99 percent to 90 percent, without performing any calculations, one can expect the confidence interval to become narrower because less area under the normal curve is needed for a lower confidence level, hence a smaller interval will still capture the true population mean.
When constructing a 98 percent confidence interval for the mean number of hours statistics students watch television, we would use the sample mean and sample standard deviation. The confidence interval formula uses the Z-score associated with the chosen confidence level and the sample's standard deviation to calculate the error bound for the interval, which, when added and subtracted from the sample mean, provides the interval range.