Question

In a survey of 800 college students in the United States, 624 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.)

( ,    )

Interpret the interval.

We are 95% confident that the true proportion of U.S. college students who believe that a student or faculty member on campus who uses language considered racist, sexist, homophobic, or offensive should be subject to disciplinary action falls within this interval.

There is a 95% chance that the true proportion of U.S. college students who believe that a student or faculty member on campus who uses language considered racist, sexist, homophobic, or offensive should be subject to disciplinary action falls within this interval.   

We are 95% confident that the mean number of U.S. college students who believe that a student or faculty member on campus who uses language considered racist, sexist, homophobic, or offensive should be subject to disciplinary action falls within this interval.

There is a 95% chance that the true proportion of U.S. college students who believe that a student or faculty member on campus who uses language considered racist, sexist, homophobic, or offensive should be subject to disciplinary action falls directly in the middle of this interval.

We are 95% confident that the true proportion of U.S. college students who believe that a student or faculty member on campus who uses language considered racist, sexist, homophobic, or offensive should be subject to disciplinary action falls directly in the middle of this interval.

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 624 / 800 = 0.78

1 - = 1 - 0.78 = 0.22

Z/2 = Z_0.025 = 1.96

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

= 1.96 (((0.78 * 0.22) / 800)

= 0.029

A 95% confidence interval for population proportion p is ,

± E  

= 0.78  ± 0.029

= ( 0.751, 0.809 )

We are 95% confident that the true proportion of U.S. college students who believe that a student or faculty member on campus who uses language considered racist, sexist, homophobic, or offensive should be subject to disciplinary action falls within this interval.