Question

Problem. Meghan Markle believes that newer apartments are more expensive than old ones in the LSU neighborhood. She took a sample of n-12 apartments and found that the sample correlation coefficient r between the monthly rent (x) and the age of apartment building (y) is r-0.576. Test the ху hypothesis that these quantities are negatively correlated. )Alternatives Select one: HP #0 H O HP0 O H 0 OH P0 o HPy0 <0 ху HPo H P0 y None of the other four ( Test statistic Select one Ot 2.228 Ot-2.501 Ot-1.796 None of the other four O Ot 1363 (i) p-value Select one: O 0.01 O 0.005 O 0.05 O 0.025 0.10 (iv) What is the conclusion if the level of significance is a-0.05? Select one oConclude H, that those quantities are negatively correlated. O Conclude H that those quantities are not negatively correlated. o Conclude H, that those quantities are negatively correlated. o Conclude H, that those quantities are not negatively correlated. O None of the other four

Answer 1

i ) we have to test the quantities are negatively correlated.

Null and alternative hypotheses are

Ho :  
pey > 0
; H1 : $\rho$ xy < 0

ii) Test statistic  

t* = r * $\sqrt$ n - 2 / $\sqrt$ 1 - r²

t* = -0.576* $\sqrt$ 12- 2 / $\sqrt$ 1- (-0.576²)

t* = - 2.228

iii) p -value for t = -2.228 and d,f = n -1 = 12-2 = 10

p-value = P( t < -2.228) d.f = 10

p-value = 0.0250

iv) Decision rule : Reject Ho if p-value < a otherwise fail to reject Ho

our p-value = 0.0250 < 0.05 , so we reject Ho

conclusion : Conclude H1 that those quantities are negatively correlated .