In a sample of 170 students at an australian university that introduced the use of plagiarism-detection software in a number of courses, 58 students indicated a belief that such software unfairly targets students. does this suggest that a majority of students at the university do not share this belief? test appropriate hypotheses at level 0.05. (let p be the proportion of students at this university who do not share this belief.)

Based on the p value obtained and using the significance level given we have so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of students who NOT belief that such software unfairly targets students is higher than 0.5 or 50% .  

Step-by-step explanation:

1) Data given and notation  

n=170 represent the random sample taken  

X=58 represent the student's who belief that such software unfairly targets students

estimated proportion of students who 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 test  

represent the significance level (no given)  

z would represent the statistic (variable of interest)  

represent the p value (variable of interest)  

p= proportion of student's who belief that such software unfairly targets students

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that that a majority of students at the university do not share this belief. :  

Null hypothesis:  

Alternative hypothesis:

We assume that the proportion follows a normal distribution.  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

   (1)  

The One-Sample Proportion Test is used to assess whether a population proportion is significantly (different,higher or less) from a hypothesized value .  

Check for the assumptions that he sample must satisfy in order to apply the test

a)The random sample needs to be representative: On this case the problem no mention about it but we can assume it.

b) The sample needs to be large enough

3) Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

4) Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level provided is . The next step would be calculate the p value for this test.  

Since is a one right side test the p value would be:  

Based on the p value obtained and using the significance level given we have so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of students who NOT belief that such software unfairly targets students is higher than 0.5 or 50% .  

step-by-step explanation: