Working Parents Probability

Question

A USA Today/CNN/Gallup survey of 378 working parents found 197 who said they spend too little time with their children because of work commitments.

a. What is the point estimate of the proportion of the population of working parents who feel they spend too little time with their children because of work commitments?

 (to 4 decimals)

b. At 95% confidence, what is the margin of error?

 (to 4 decimals)

c. What is the 95% confidence interval estimate of the population proportion of working parents who feel they spend too little time with their children because of work commitments (to 4 decimals)?

Answer 1

a. The point estimate of the proportion of the population of working parents who feel they spend too little time with their children because of work commitments is:

197/378 = 0.5212 (to 4 decimals)

b. At 95% confidence, the margin of error can be calculated using the formula:

margin of error = z* * sqrt(p*(1-p)/n)

where z* is the z-score corresponding to the 95% confidence level, p is the point estimate, and n is the sample size.

Using a table of z-scores or a calculator, we find that the z-score corresponding to the 95% confidence level is 1.96.

Plugging in the values, we get:

margin of error = 1.96 * sqrt(0.5212*(1-0.5212)/378) ≈ 0.0494 (to 4 decimals)

c. The 95% confidence interval estimate can be calculated using the formula:

confidence interval = point estimate ± margin of error

Plugging in the values, we get:

confidence interval = 0.5212 ± 0.0494

The lower bound of the interval is:

0.5212 - 0.0494 = 0.4718

The upper bound of the interval is:

0.5212 + 0.0494 = 0.5706

Therefore, the 95% confidence interval estimate of the population proportion of working parents who feel they spend too little time with their children because of work commitments is (0.4718, 0.5706) (to 4 decimals).