QUESTION IN DESCRIPTION *AP STATS

Question

For some people, mistletoe is a symbol of romance. Mesquite trees, however, have no love for the parasitic plant that attaches itself and steals nutrients from the tree. To estimate the proportion of mesquite trees in a desert park that are infested with mistletoe, a random sample of mesquite trees was randomly selected. After inspecting the trees in the sample, the park supervisor calculated a 95% confidence interval of 0.2247 to 0.5753.

a. Find the point estimator for the interval

b. Find the margin of error

c. Interpret the confidence level

d. Calculate the sample size used to create the interval

Answer 1

95% confidence interval of 0.2247 to 0.5753.

a. Find the point estimator for the interval

(0.2247 + 0.5753)/2 = 0.4

b. Find the margin of error

(0.5753 - 0.2247)/2 = 0.1753

c. Interpret the confidence level

95% confidence level means that there is a 95% probability the true population proportion is between 0.2247 and 0.5753.

d. Calculate the sample size used to create the interval

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

0.1753 = 1.96 * sqrt(0.4 * 0.6/n)

0.0894 = sqrt(0.24/n)

0.008 = 0.24/n

n = 0.24/0.008

n = 30