Given data
For southlake resident
n1 = 17 ( sample size for southlake resident )
1 = 9.2 ( sample mean i.e mean length of owenership for southlake resident )
s1 = 2.9 ( sample standard deviation for southlake resident )
For Northwood resident
n2 = 15
2 = 7.4 ( sample mean i.e mean length of owenership for Northwood resident )
s2 = 2.1 ( sample standard deviation for Northwood residentt )
To Test :-
H0 : u1 u2 [ Southlake resident may not owned their homes for longer period than Northwood residentt ]
H1 : u1 > u2 [ Southlake resident may owned their homes for longer period than Northwood residentt ]
Test Statistics TS :-
TS =
Calculation -
SE =
where
=
=
= 6.543333 { after calculation }
Thus
SE =
=
SE = 0.906159 { after calculation }
So we have
1 = 9.2 ; 2 = 7.4 ; SE = 0.906159
TS =
TS =
TS = 1.986406
So calculated test statistics value is TS = 1.986406
To find t-critical value :-
Since alternative hypothesis is of " > " type , so this is one-tail test , and hence its critical t-value will be given by , where is t-distributed with n1+n2-2 = 17+15-2 = 30 degree of freedom with = 0.05
Now can be obtained from statistical book or more accuratly from any software like R/Excel .
From R
> qt(1-0.05,df=30)
[1] 1.697261
Hence t-critical value = 1.697261
Rejection criteria ( Decision Rule ) :-
We reject null hypothesis is calculated test statistics is greater than t-critical value
Now here we have TS = 1.986406 > 1.697261
i.e TS >
Since , test statistics value TS greater than t-critical value , we reject null hypothesis at 0.05 level of significance .
Conclusion :-
We reject null hypothesis H0 , and hence we conclude that , Southlake resident owned their homes for longer period of time compare to resident in the Northwood area .
The Metro Real Estate Association is preparing a pamphlet that they feel might be of interest...
The Metro Real Estate Association is preparing a pamphlet that they feel might be of interest to prospective home buyers in the Southlake and Northwood areas of the city. One item if interest is the length of time the seller occupied the home. A sample of 17 homes sold recently in Southlake revealed that the mean length of ownership was 9.2 years with a standard deviation of 2.9 years. A sample of 15 homes in Northwood revealed that the mean...
The Metro Real Estate Association is preparing a pamphlet that they feel might be of interest to prospective home buyers in the Southlake and Northwood areas of the city. One item if interest is the length of time the seller occupied the home. A sample of 17 homes sold recently in Southlake revealed that the mean length of ownership was 9.2 years with a standard deviation of 2.9 years. A sample of 15 homes in Northwood revealed that the mean...
The Metro Real Estate Association is preparing a pamphlet that they feel might be of interest to prospective home buyers in the Southlake and Northwood areas of the city. One item if interest is the length of time the seller occupied the home. A sample of 17 homes sold recently in Southlake revealed that the mean length of ownership was 9.2 years with a standard deviation of 2.9 years. A sample of 15 homes in Northwood revealed that the mean...
Please read the article and answer about questions. You and the Law Business and law are inseparable. For B-Money, the two predictably merged when he was negotiat- ing a deal for his tracks. At other times, the merger is unpredictable, like when your business faces an unexpected auto accident, product recall, or government regulation change. In either type of situation, when business owners know the law, they can better protect themselves and sometimes even avoid the problems completely. This chapter...