Question

A random sample of 78 students were interviewed and 59 said they would vote for a democrat in the 2008 election.

1. Let p represent the proportion of all students at this college who will vote for a democrat. Find a point estimate p for p.

2. Find a 90% confidence interval for p.

3. What assumptions are required for the calculations of part (b)? Do you think these assumptions are satisfied? Explain

4. How many more students should be included in the sample of 90% sure that a point estimate p will be within a distance of 0.05 from p.

Answer 1

1)

Sample size = n = 78

x = 59

Sample proportion is

2)

We have to construct 90% confidence interval for the population proportion.

Formula is

Here E is a margin of error.

Zc = 1.64

So confidence interval is ( 0.7564 - 0.0797 , 0.7564 + 0.0797) => ( 0.6767 , 0.8361)

3)

Assumptions:

• The sample is a simple random sample.
• The normal distribution is used to approximate the distribution of sample proportions.

Yes, the assumptions are satisfied.

4)

Margin of error = E = 0.05

Confidence level = C = 0.90

Zc = 1.64   ( Using z table)

p = 0.7564

We have to find the sample size (n)