Question

five-year-old census recorded that 20% of the families in a large community lived below the poverty level. To determine whether this percentage has changed, a random sample of 400 families is studied and 80 are found to be living below the poverty level.

1.Construct a 98% confidence interval for the percentage of families earning income below the poverty level.

2.Does this finding indicate that the current percentage of families earning income below the poverty level has changed from what it was five years ago? Use a = 0.05

3.Calculate the P-value for the hypothesis testing in 2. and make a conclusion of this with a = 0.05

4.Suppose a researcher would like to estimate the proportion of families earning income below the poverty level. He wants to estimate, with a margin of error within 0.03 at the 90% confidence. How large a sample size must be taken?

Answer 1