Monthly rent paid by undergraduates and graduate students. Undergraduate Student Rents (n = 10) 760 770 890 660 730 790 790 690 1,060 680 Graduate Student Rents (n = 12) 1,080 920 930 880 720 920 740 830 960 880 860 870 Click here for the Excel Data File (a) Construct a 99 percent confidence interval for the difference of mean monthly rent paid by undergraduates and graduate students, using the assumption of unequal variances. (Use Minitab. Round your final answers to 3 decimal places.) The 99% confidence interval is from to (b) What do you conclude? We cannot conclude there is a significant difference in means for undergraduate and graduate rent. We can conclude there is a significant difference in means for undergraduate and graduate rent.

(a) 99% Confidence interval =  [ -230.11 , 29.11 ]

(b) We cannot conclude there is a significant difference in means for undergraduate and graduate rent.

Step-by-step explanation:

We are given the Monthly rent paid by undergraduates and graduate students.

Undergraduate Student Rents (n = 10) : 760, 770, 890, 660, 730, 790, 790, 690, 1,060, 680

Graduate Student Rents (n = 12) : 1,080, 920, 930, 880, 720, 920, 740, 830, 960, 880, 860, 870

Firstly let = Sample mean of Undergraduate Student Rents

                          = Sum of all rent values ÷ n = 782

= variance of Undergraduate Student Rents = = 14018

= Sample mean of Graduate Student Rents = 882.5

= variance of Graduate Student Rents = = 9111.4

The pivotal quantity used here for confidence interval is;

                          ~

where,

P(-2.845 < < 2.845) = 0.99

P(-2.845 < < 2.845) = 0.99

P(-2.845*<<2.845* ) = 0.99

P( - 2.845* < < + 2.845* ) = 0.99

99% Confidence interval for =

[ - 2.845* , + 2.845* ]

[(782 - 882.5) - 2.845* , (782 - 882.5) + 2.845* ]

 =  [ -230.11 , 29.11 ]

(b) After seeing the 99% confidence interval for the difference of mean monthly rent paid by undergraduates and graduate students, we cannot conclude that there is a significant difference in means for undergraduate and graduate rent because in the above interval 0 lies in between them .

irrational, cannot