(Sec. 8.4) In a sample of 165 students at an Australian university that introduced the use of plagiarism-detection software in a number of courses, 55 students indicated a belief that such software unfairly targets students. Does this suggest that a majority of students at the university do not believe that it unfairly targets them? Test the appropriate hypotheses at the 5% significance level.

The p value for this case is given by:

Since the p value is lower than the significance level we have enough evidence to conclude that the true proportion is significantly higher than 0.5 at 5% of significance.

Step-by-step explanation:

Information given

n=165 represent the random sample selected

55 represent the students indicated a belief that such software unfairly targets students

X =165-55= 110 represent students who NOT belief that such software unfairly targets students

estimated proportion of  students who NOT belief that such software unfairly targets students

is the value that we want to check

represent the significance level

z would represent the statistic

represent the p value

System of hypothesis

We want to check if the majority of students at the university do not believe that it unfairly targets them, and the system of hypothesis are:

Null hypothesis:  

Alternative hypothesis:  

The statistic for this case is given by:

(1)  

After replace we got:

The p value for this case is given by:

Since the p value is lower than the significance level we have enough evidence to conclude that the true proportion is significantly higher than 0.5 at 5% of significance.

24+x=y

step-by-step explanation: