56 - The Practice of Statistics for AP

Question

Reporting cheating What proportion of students

are willing to report cheating by other students? A

student project put this question to an SRS of 172

undergraduates at a large university: “You witness two

students cheating on a quiz. Do you go to the professor?”

The Minitab output below shows the results of a

significance test and a 95% confidence interval based

on the survey data.18

(a) Define the parameter of interest.

(b) Check that the conditions for performing the significance test are met in this case.

(c) Interpret the P-value in context.

(d) Do these data give convincing evidence that the actual population proportion differs from 0.15? Justify your answer with appropriate evidence.

Step-by-Step Solution

Answer

Part (a) Population proportion

Part (b) If p-value is less than 0.05 implies the test is significant. 

Part (c)  0.146>0.05, Test is not significant. 

Part (d) No conclusion can be drawn  

Part (a) Step 1. Parameter of interest

The Minitab output represents the confidence interval of the population proportion. So, the parameter of interest is the population proportion. 

Part (b) Step 1. Decision Criteria

The criteria for testing whether the hypothesis test is significant or not. In other words, if the probability of rejecting the null hypothesis is less than 0.05 implies that the test is significant.

Part (c) Step 1. Interpretation

It can be observed that the p-value is less than 0.05, that is, 

$0.146>0.05$

As a result, the test is insignificant as there is not enough evidence to reject the null hypothesis. 

Part (d) Step 1 Conclusion

It can be observed that there is not enough evidence to reject the null hypothesis and the test is not significant. So, no conclusion can be made about the claim.