Question

In a survey of 1037 adults from the US age 65 and over, 643 were concern about getting flu.

(a) Find a point estimate for the population proportion P of those concerned about getting the flu.

(b) Construct a 95% confidence interval for the population proportion. What does this interval say to you?

(c) Find the minimum sample size needed to estimate the population proportion at the 99% confidence level in order to ensure that the estimate is accurate within 4% of the population proportion.

Answer 1

Solution :

Given that,

(a)

Point estimate = sample proportion = = x / n = 643 / 1037 = 0.620

1 - = 1 - 0.620 = 0.38

Z/2 = 1.96

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 1.96 * (((0.620 * 0.38) / 1037)

Margin of error = E = 0.030

(b)

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.620 - 0.030 < p < 0.620 + 0.030

0.590 < p < 0.650

The 95% confidence interval for the population proportion p is : 0.590 , 0.620

(c)

= 1 - = 0.5

margin of error = E = 0.04

  Z/2 = 2.576

sample size = n = (Z / 2 / E )2 * * (1 - )

= (2.576 / 0.04)2 * 0.5 * 0.5

= 1037

sample size = 1037