Question

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Suppose we would like to make a confidence interval for the proportion of Americans who support "gun control Which of the following statements is TRUE? Select one: O a. The exact probability that a confidence interval contains the population proportion is always higher for a 95% confidence interval than a 90% confidence interval. Cross out o b . A 90% confidence interval obtained from a random sample of 100 people has a better chance of containing the population proportion than a 90% confidence interval obtained from a random sample of 50 people cross out O c. A 95% confidence interval obtained from a random sample of 100 people has a lower chance of containing the population proportion than a 95% confidence interval obtained from a random sample of 50 people. cross out d. A 90% confidence interval is narrower than a 95% confidence interval if both confidence intervals use the same sample size. cross out e. A 99% confidence interval is narrower than a 95% confidence interval if both confidence intervals use the same sample size cross out

Answer 1

a) Since a 90% confidence interval has a wider range and includes the entire range of the 95% confidence interval, this statement is False

b) False, all 90% confidence intervals have a 90% chance of yielding an interval that contains the population proportion

c) Same as above: False, all 95% confidence intervals have a 95% chance of yielding an interval that contains the population proportion

d) True, a 90% is narrower since you are less certain that the proportion will lie in that range than a 95% confidence interval

e) False, a 99% is wider than a 95% interval if using the same data set since you want to be more confidence you need a wider range for the proportion to be in that range.