Question

In a survey of 800 college students in the

United States, 632 indicated that they believe that a student or faculty member on campus who uses language considered racist, sexist, homophobic, or offensive should be subject to disciplinary action. Assuming that the sample is representative of college students in the United States, construct a 95% confidence interval for the proportion of college students who have this belief. (Use a table or technology. Round your answers to three decimal places.)

Answer 1

Solution :

Given that,

n = 800

x = 632

Point estimate = sample proportion = = x / n = 632 / 800 = 0.79

1 - = 1 - 0.79 = 0.21

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z_{0.025 = 1.960}

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.96 (((0.79 * 0.21) / 800 )

= 0.028

A 95% confidence interval for population proportion p is ,

± E

= 0.79 ± 0.028

= ( 0.762, 0.818 )