1. An article in the Washington Post on March 16, 1993 stated

that nearly 45 percent of all Americans have brown eyes. A random

sample of

*n*=84 C of I students found 31 with brown eyes.

We test

*H0* :*p*=.45

*H**a*:*p*â‰ .45

(a) What is the

*z*-statistic for this test?

(b) What is the P-value of the test?

2. Dylan wants to determine a 95 percent confidence interval for

the true proportion of high school students in the area who attend

their home basketball games. How large of a sample must he have to

get a margin of error less than 0.04? [To find n, use the value p*

= 1/2 for the sample proportion and the values for z* from a

z-table or t-table.]

[Round to the smallest integer that works.] n =

3. For each problem, select the best response.

(a) A newspaper conducted a statewide survey concerning the 1998

race for state senator. The newspaper took a SRS of 1200 registered

voters and found that 620 would vote for the Republican candidate.

Let *p* represent the proportion of registered voters in the

state who would vote for the Republican candidate. A 90 percent

confidence interval for *p* is:

**A.** 0.517Â±0.024

**B.** 0.517Â±0.014

**C.** 0.517Â±0.249

**D.** 0.517Â±0.028

(b) A radio talk show host with a large audience is interested

in the proportion *p* of adults in his listening area who

think the drinking age should be lowered to 18. He asks, ‘Do you

think the drinking age should be reduced to 18 in light of the fact

that 18 year olds are eligible for military service?’ He asks

listeners to phone in and vote ‘yes’ if they agree the drinking age

should be lowered to 18, and ‘no’ if not. Of the 100 people who

phoned in, 70 answered ‘yes.’ Which of the following assumptions

for inference about a proportion using a confidence interval are

violated?

**A.** The sample size is large enough so that the

count of successes np^ is 15 or more.

**B.** The population is at least ten times as

large as the sample.

**C.** The data are an SRS from the population of

interest.

**D.** The sample size is large enough so that the

count of failures

*n*(1âˆ’*p* )is 15 or more.

(c) A newspaper conducted a statewide survey concerning the 1998

race for state senator. The newspaper took a SRS of 1200 registered

voters and found that 620 would vote for the Republican candidate.

Let *p* represent the proportion of registered voters in the

state who would vote for the Republican candidate. How large a

sample *n* would you need to estimate *p* with a

margin of error 0.01 with 95 percent confidence? Use the guess

*p*=.5 as the value of *p*

**A.** 9604

**B.** 49

**C.** 1500

**D.** 4800