Question

answer B

A department of education reported that in 2007, 66% of students enrolled in college or a trade school within 12 months of graduating from high school. In 2013, a random sample of 320 individuals who graduated from high school 12 months prior was selected. From this sample, 236 students were found to be enrolled in college or a trade school. Complete parts a through c below. a. Construct a 95% confidence interval to estimate the actual proportion of students enrolled in college or a trade school within 12 months of graduating from high school in 2013. A 95% confidence interval to estimate the actual proportion has a lower limit of 0.690 and an upper limit of 0.786 . (Round to three decimal places as needed.) b. What is the margin of error for this sample? The margin of error is (Round to three decimal places as needed.)

Answer 1

Part b

We have

Margin of error = Z* sqrt(p̂*(1 – p̂)/n)

We are given

Number of items of interest = x = 236

Sample size = n = 320

Sample proportion = p̂ = x/n = 236/320 = 0.7375

Confidence level = 95%

Critical Z value = 1.96

(by using z-table)

Margin of error = Z* sqrt(p̂*(1 – p̂)/n)

Margin of error = 1.96* sqrt(0.7375*(1 - 0.7375)/320)

Margin of error = 0.048209

Margin of error = 0.048

The margin of error is 0.048.