4
a)
Home heating costs Vs Size
Hypothesis
H0: There is no significant relationship between home heating cost and size
H1: There is a significant relationship between home heating cost and size
Significance=0.05/2=0.025
Z=1.96
Decision criteria; Reject H0 if t static is greater than 1.96 and accept H1
Observed value of t statistics=3.78>1.96, we reject H0 and accept H1
Observed value of P-value=0.006
Decision;
There is a significant relationship between home heating cost and size


Home heating costs vs Windows 
Hypothesis
H0: There is no significant relationship between home heating cost and windows
H1: There is a significant relationship between home heating cost and windows
Significance=0.05/2=0.025
Z=1.96
Decision criteria; Reject H0 if t static is greater than 1.96 and accept H1
Observed value of t statistics=1.621.96, we reject H0 and accept H1
Observed value of P-value=0.0316
Decision;
There is a significant relationship between home heating cost and windows