Question

According to the Census Bureau, 3.36 people reside in the typical American household. A sample of 27 households in Arizona retirement communities showed the mean number of residents per household was 2.70 residents. The standard deviation of this sample was 1.25 residents. At the .10 significance level, is it reasonable to conclude the mean number of residents in the retirement community household is less than 3.36 persons?

  

a.	State the null hypothesis and the alternate hypothesis. (Round your answer to 2 decimal places.)

H0: μ ≥
H1: μ <

  

b.	State the decision rule for .10 significance level. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)

Reject H0 if t <

  

c.	Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)

Value of the test statistic

  

d.	Is it reasonable to conclude the mean number of residents in the retirement community household is less than 3.36 persons?

(Click to select)  Reject  Fail to reject  H0. Mean number of residents  (Click to select)  is not necessarily  is necessarily  less than 3.36 persons.

Answer 1

Given that,
population mean(u)=3.36
sample mean, x =2.7
standard deviation, s =1.25
number (n)=27
null, Ho: μ=3.36
alternate, H1: μ<3.36
level of significance, α = 0.1
from standard normal table,left tailed t α/2 =1.315
since our test is left-tailed
reject Ho, if to < -1.315
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =2.7-3.36/(1.25/sqrt(27))
to =-2.74
| to | =2.74
critical value
the value of |t α| with n-1 = 26 d.f is 1.315
we got |to| =2.74 & | t α | =1.315
make decision
hence value of | to | > | t α| and here we reject Ho
p-value :left tail - Ha : ( p < -2.7436 ) = 0.00543
hence value of p0.1 > 0.00543,here we reject Ho
ANSWERS
---------------
a.
null, Ho: μ=3.36
alternate, H1: μ<3.36
b.
decision: reject Ho
c.
test statistic: -2.74
critical value: -1.315
p-value: 0.00543
d.
we have enough evidence to support the claim that the mean number of residents in the retirement community household is less than 3.36 persons