Question

1.)We wish to estimate what percent of adult residents in a certain county are parents. Out of 500 adult residents sampled, 55 had kids. Based on this, construct a 90% confidence interval for the proportion p of adult residents who are parents in this county.

Provide the point estimate and margin of error. Give your answers as decimals, to three places.
p=____±± _____

2.)You measure 27 textbooks' weights, and find they have a mean weight of 38 ounces. Assume the population standard deviation is 4.4 ounces. Based on this, construct a 95% confidence interval for the true population mean textbook weight.
Give your answers as decimals, to two places
_____< μμ < ______

3.If n=22, ¯xx¯(x-bar)=44, and s=2, find the margin of error at a 90% confidence level
Give your answer to two decimal places.

Answer 1

To construct a 90% confidence interval for the proportion of adult residents who are parents, calculate the point estimate by dividing the number of adults who had kids by the total number of adults sampled. Then, use the formula to calculate the margin of error. The confidence interval can be determined by adding and subtracting the margin of error from the point estimate.

Step-by-step explanation:

To construct a 90% confidence interval for the proportion of adult residents who are parents in the county, we first find the point estimate, which is the proportion of adults sampled who had kids. The point estimate is calculated by dividing the number of adults who had kids by the total number of adults sampled. In this case, the point estimate is 55/500 = 0.11

The margin of error is calculated using the formula: Margin of Error = Z * sqrt((p * (1-p)) / n), where Z is the critical value for a given confidence level, p is the point estimate, and n is the sample size. For a 90% confidence level, the critical value Z is approximately 1.645. Plugging in the values, we get Margin of Error = 1.645 * sqrt((0.11 * (1-0.11)) / 500) = 0.038

Therefore, the 90% confidence interval for the proportion of adult residents who are parents in the county is 0.11 ± 0.038, or 0.072 to 0.148.