Answer the following questions about confidence intervals.
(a) What happens to a confidence interval as sample size​increases, assuming everything else stays the​ same?
The width of the interval​ decreases, since the standard error decreases.The center of the interval​ decreases, since the standard error increases. The center of the interval​increases, since the standard error decreases.The width of the interval​ increases, since the standard error increases.
(b) If we want to use a larger confidence level when creating a confidence interval for a population​ mean, which of the following happens to our confidence​ interval?
The interval gets​ wider, since the standard error decreases.The interval gets​ narrower, since the​ t-value required to capture a larger proportion of the sampling distribution of the sample mean gets smaller. The interval gets​ narrower, since the standard error decreases.The interval gets​ wider, since the​ t-value required to capture a larger proportion of the sampling distribution of the sample mean gets larger.
(c) What does the margin of error in a confidence interval for a population mean​ describe?
It describes the difference between the sample mean and the population mean due to calculation errors by the researchers. It describes the difference between the sample mean and the population mean. Due to the random sampling​ method, different sample means will be different. It describes the difference between the sample mean and the population​ mean, due to taking​ non-random samples involving voluntary response or convenience sampling.It describes how often researchers make a mistake due to response bias or​ non-response bias.
(d) Why do we use a z-score from a normal distribution in constructing large-sample confidence intervals for a proportion?
For large random samples the data distribution is approximately normal.For any n we use the​ t-distribution to get a confidence​interval, and for large n the​ t-distribution looks like the standard normal distribution. For large random samples the sampling distribution of the sample proportion is approximately normal.The population distribution is normal for large samples.
(e) True or false: The confidence interval for a mean with a random sample of size n​ = 2000 is invalid if the population distribution is bimodal.
TrueFalse