91Ó°ÊÓ

Which of the following are unbiased estimators for the corresponding population parameters? I. Sample means II. Sample proportions III. Difference of sample means IV. Difference of sample proportions (A) None are unbiased. (B) I and II only (C) I and III only (D) III and IV only (E) All are unbiased.

Assume the given distributions are roughly normal. A coffee machine can be adjusted to deliver any fixed number of ounces of coffee. If the machine has a standard deviation in delivery equal to 0.4 ounce, what should be the mean setting so that an 8-ounce cup will overflow only \(0.5 \%\) of the time? (A) \(8-0.995(0.4)\) (B) \(8+1.96(0.4)\) (C) \(8-1.96(0.4)\) (D) \(8+2.576(0.4)\) (E) \(8-2.576(0.4)\)

A study is to be performed to estimate the proportion of voters who believe the economy is "heading in the right direction." Which of the following pairs of sample size and population proportion \(p\) will result in the smallest variance for the sampling distribution of \(\hat{p} ?\) (A) \(n=100\) and \(p=0.1\) (B) \(n=100\) and \(p=0.5\) (C) \(n=100\) and \(p=0.99\) (D) \(n=1000\) and \(p=0.1\) (E) \(n=1000\) and \(p=0.5\)