Real estate taxes are used to fund local education institutions, police protecti

Question

Real estate taxes are used to fund local education institutions, police protection, libraries, and other local public services. A household's real estate tax bill is based on the value of the house. In a recent year, the mean real estate tax bill per $1,000 assessed value for all households in a certain country was $9.07 . A random sample of 50 rural households results in a sample mean real estate bill per $1,000 assessed value of $6.45 with a standard deviation of $6.12 . Use the level of significance alpha equals0.05.

Conduct a hypothesis test using the P-value approach and a level of significance of .05 to determine if the evidence suggests the mean real estate bill for rural households per $1,000 assessed value differs from that of all households.

Explanation / Answer

Given that,
population mean(u)=9.07
sample mean, x =6.45
standard deviation, s =6.12
number (n)=50
null, Ho: =9.07
alternate, H1: !=9.07
level of significance, = 0.05
from standard normal table, two tailed t /2 =2.01
since our test is two-tailed
reject Ho, if to < -2.01 OR if to > 2.01
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =6.45-9.07/(6.12/sqrt(50))
to =-3.027
| to | =3.027
critical value
the value of |t | with n-1 = 49 d.f is 2.01
we got |to| =3.027 & | t | =2.01
make decision
hence value of | to | > | t | and here we reject Ho
p-value :two tailed ( double the one tail ) - Ha : ( p != -3.0272 ) = 0.0039
hence value of p0.05 > 0.0039,here we reject Ho
ANSWERS
---------------
null, Ho: =9.07
alternate, H1: !=9.07
test statistic: -3.027
critical value: -2.01 , 2.01
decision: reject Ho
p-value: 0.0039
mean real estate bill for rural households per $1,000 assessed value differs from that of all households

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