Interval Estimation for Proportion.
In a randoms sample survey, 250 young professionals who
Work in Makati are asked whether they commuted to the city or
bought their own car. If 88 of them commuted to work.
construct a 99% confidence interval for the true proportion who
commute to work.
In a randoms sample survey, 250 young professionals who
Work in Makati are asked whether they commuted to the city or
bought their own car. If 88 of them commuted to work.
construct a 99% confidence interval for the true proportion who
commute to work.
Answers & Comments
Answer:
To construct a 99% confidence interval for the true proportion who commute to work, we can use the formula:
Confidence Interval = Sample Proportion ± Margin of Error
where:
Sample Proportion = Number of individuals who commute / Total sample size
Margin of Error = Z * sqrt((Sample Proportion * (1 - Sample Proportion)) / Sample Size)
Given the information provided:
Number of individuals who commute = 88
Total sample size = 250
First, calculate the sample proportion:
Sample Proportion = 88 / 250 = 0.352
Next, calculate the margin of error. To do this, we need the critical value (Z) for a 99% confidence level. Since the sample size is large (n > 30), we can use the standard normal distribution. The critical value for a 99% confidence level is approximately 2.576.
Margin of Error = 2.576 * sqrt((0.352 * (1 - 0.352)) / 250)
Calculating this:
Margin of Error = 2.576 * sqrt(0.235936 / 250) ≈ 0.067
Finally, construct the confidence interval:
Confidence Interval = 0.352 ± 0.067
The 99% confidence interval for the true proportion of young professionals who commute to work is approximately 0.285 to 0.419. This means that we are 99% confident that the true proportion of young professionals who commute to work falls within this range based on the sample data.