Question

A university is interested in whether there's a difference between students who live on campus and students who live off campus with respect to absenteeism. Over one semester, researchers take random samples of on-campus and off-campus students and record the following number of classes each student misses.

On-campus: (3, 4, 0, 6, 2, 1, 3, 3, 5, 2, 4, 4, 6, 5, 2)

Off-campus: (6, 5, 2, 6, 2, 0, 7, 8, 1, 7, 2, 6, 5, 3, 2)

a) Using a 5% significance level, test whether or not there is a difference between the two groups.

b) Compute and interpret a 95% confidence interval for the difference between the number of classes missed by each group of students. Make sure to show your plug-ins.

c) Based on the confidence interval you created in part B, draw a conclusion about the differences between the means of the two groups.

Answer 1

a ) Define , : Population mean of the number of classes missed by on campus students .

   : Population mean of the number of classes missed by off campus students .

To test :

Test statistic :

where , and

Degrees of freedom = 28

We reject the null hypothesis or H₀ if the observed value of , where ,

The value of the test statistic :

Critical value :  

Now ,

Hence we accept the null hypothesis or H₀ .

Thus we do not have sufficient evidence to support the claim that there is a difference between students who live on campus and students who live off campus with respect to absenteeism.

b ) The 95 % confidence interval of is :

where ,

and   ,

Required confidence interval :

c ) Since the 95 % confidence interval contains 0 , hence we can conclude that there is no difference between students who live on campus and students who live off campus with respect to absenteeism .