8.4.33) A department of education reported that in 2007, 64% of students enrolle

Question

8.4.33) A department of education reported that in 2007, 64% of students enrolled in college or a trade school within 12 months of graduating from high school. In 2013, a sample of 320 individuals who graduated from high school 12 months prior was selected. From this sample, 204 students were found to be enrolled in college or a trade school.

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 ___ and and an upper limit of ___ . (Round to three decimal places as needed.)

b. What is the margin of error for this sample?

8.4.31) Determine the margin of error for a confidence interval to estimate the population proportion for the following confidence levels with a sample proportion equal to 0.45 and n=129.

a. 90% b. 95% c. 97%

(Round to three decimal places as needed.)

a. The margin of error for a confidence interval to estimate the population proportion for the 90% confidence level is

b. The margin of error for a confidence interval to estimate the population proportion for the 95% confidence level is

c. The margin of error for a confidence interval to estimate the population proportion for the 97% confidence level is

Explanation / Answer

here p=204/320 =0.66375

hence std error =(p(!-p)/n)1/2 =0.0269

for 95% CI, z=1.96

hence Confidence interval =p -/+ z*std error =0.5848 ; 0.6902

8.4.31)a)as margin of error =z*std error

hence from above a) for 90% z=1.6449 ; margin of error =0.072

for 95% z=1.96 ; margin of errror =0.086

for 97%; z=2.17 ;margin of errror =0.095

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