Monthly rent paid by undergraduates and graduate students. Undergraduate Student Rents (n = 10) 760 770 890 660 730 790 790 690 1,060 680 Gr

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3 months 2021-11-10T00:20:39+00:00 1 Answer 0 views 0

(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 .