Question

QUESTION 2

Part 1

In a survey of 800 college students in the United States, 608 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.)

(___,___)

PART B

Interpret the interval. Chose 1

A. 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.

B. 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.    

C. 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.

D. 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.

E. 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: In a survey of 800 college students in the United States, 608 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.

Thus sample size =n = 800

x = Number of college students in the United States 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.

x = 608

thus sample proportion is:

c = confidence level = 95%

Part a) Construct a 95% confidence interval for the proportion of college students who have this belief.

Formula;

where

We need to find z_c value for c=95% confidence level.

Find Area = ( 1 + c ) / 2 = ( 1 + 0.95) /2 = 1.95 / 2 = 0.9750

Look in z table for Area = 0.9750 or its closest area and find z value.

Area = 0.9750 corresponds to 1.9 and 0.06 , thus z critical value = 1.96

That is : Z_c = 1.96

thus

Thus

Part b) Interpret the interval.

D. 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.

Since confidence interval is the estimate of population parameters( here population proportion),correct option is D.