(E)
- Why is t used instead of z as the critical value in a confidence interval for a mean?
(A) Because means are continuous, not discrete like proportions.
(B) Because means are greater than proportions.
(C) Because we are using s to estimate σ .
(D) Because we are using to estimate μ .
(E) Because all confidence intervals require t .
A polling company reported that 38% of Americans approve of a particular policy, with a margin of
error of 4 percentage points and 95% confidence. What is the best interpretation of that margin of
error?
(A) In 95% of similar polls, the sample proportion would fall within 4 percentage points of 38%.
(B) In 95% of similar polls, the sample proportion would fall within 4 percentage points of the
proportion of all Americans who approve of the policy.
(C) In 95% of similar polls, 4% of the time, 38% of people would approve of the policy.
(D) The survey result is wrong 4% of the time, with 95% confidence.
(E) The survey is correct 95% of the time and incorrect 4% of the time.
- A particular skin condition clears up on its own after about a month in about 40% of cases. A new
topical medication has been developed to increase the proportion of patients who are cured after
about a month, but the new medication would cost money. The null hypothesis is that the proportion of
patients cured with the new medication is the same as the proportion cured with a placebo, and the
alternative hypothesis is that the proportion of patients cured with the new medication is greater than
the proportion cured with the placebo. In this situation, the consequence of a Type II error would be
(A) people paying more for a medication that does not help them.
(B) people not having access to a medication that would help them.
(C) the medication not being as effective as it should be.
(D) the medication being given to the wrong patients.
(E) the proportion of patients cured with the new medication turning out to be less than the
proportion cured with the placebo.