Question

In a sample of 171 students at an Australian university that introduced the use of plagarism-detection software in a number of

Irn a sample of 171 students at an Australian university Lidl introduced the use of plagiarism-detection suftware i a number of courses, 54 students indicated a belief thal such sotware unfairly Largels students. Dues this suggest that d midjurity 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) State tha appropriate hypothasas H0: ρ = 0.50 0.30 Ho: ρ = 0.50 Ho: ρ=0.50 H: P0.50 Ho: ρ > 0.50 Calculate th test statistic and datamine the pvalua. (Round your test statistic to two ded mal places and your p-valua to four dedmal places.) P-value - what can you conclude? O Reject the null hypothesis. There is sufficient evidence that more than 20% of all students do not share the belief that the plagiarism detection software unfairly targets students O Do not reject the null hypothesis. There is sufficient evidence that more than sa% of all students do not shar。the ballef that the plagiarism-datactlan ware unfaity targets students. O Reject the null hypothesis. here is not sufficient evidence that more than 50% of all students do not share the belief that the plagiarism-detection software unfairly targets students. O Do not reject the null hypothesis. There is not suffidant evidence that more than 50% of all students do not share the belof that tha plagiarism-detection software unfairly targets students. You may necd to usa the appropriate table in the Appendix of Tables to answer this queztion

Answer 1

The hypotheses

$H0:p =0.50$

$Ha:p<0.50$

Test statistic

Vp1

$\hat{p}= 1-54/171 = 0.68$

Therefore,

z = 5.05

P value < 0.0001

Since P value is very small ( P value < 0.05) , we reject H0.

Conclusion

Reject the null hypothesis. There is sufficient evidence that more than 50% of all students donot share the belief that the plagiarism detection software unfairly targets students .