Question

A USA Today/CNN/Gallup survey of 365 working parents found 202 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 becaus of work commitments (to 4 decimals)?

Answer 1

a. Point estimate of the proportion: 0.5533

b. Margin of error at 95% confidence: 0.0446

c. 95% confidence interval estimate: (0.5087, 0.5979)

Step-by-step explanation:

a. The point estimate of the proportion is calculated by dividing the number of working parents who feel they spend too little time with their children (202) by the total surveyed (365), resulting in a proportion of approximately 0.5533.

b. The margin of error at 95% confidence is determined using the formula for proportions:
`\( \text{Margin of Error} = Z * \sqrt{(p(1-p))/(n)} \)`, where Z is the critical value for a 95% confidence interval (1.96), p is the point estimate proportion (0.5533), and n is the sample size (365). Calculating this yields a margin of error of approximately 0.0446.

c. The 95% confidence interval estimate is constructed around the point estimate proportion, accounting for the margin of error. It is calculated by subtracting and adding the margin of error from the point estimate: (0.5533 - 0.0446