According to the Census Bureau, 3.26 people reside in the typical American house

Question

According to the Census Bureau, 3.26 people reside in the typical American household. A sample of 26 households in Arizona retirement communities showed the mean number of residents per household was 2.89 residents. The standard deviation of this sample was 1.25 residents. At the .05 significance level, is it reasonable to conclude the mean number of residents in the retirement community household is less than 3.26 persons?

a. State the null hypothesis and the alternate hypothesis. (Round your answer to 2 decimal places.) H0: H1: <

b. State the decision rule for .05 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 3.26 persons? (Click to select)RejectFail to reject H0. Mean number of residents (Click to select)is necessarilyis not necessarily less than 3.26 persons.

Explanation / Answer

Given that,
population mean(u)=3.26
sample mean, x =2.89
standard deviation, s =1.25
number (n)=26
null, Ho: >3.26
alternate, H1: <3.26
level of significance, = 0.05
from standard normal table,left tailed t /2 =1.708
since our test is left-tailed
reject Ho, if to < -1.708
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =2.89-3.26/(1.25/sqrt(26))
to =-1.509
| to | =1.509
critical value
the value of |t | with n-1 = 25 d.f is 1.708
we got |to| =1.509 & | t | =1.708
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value :left tail - Ha : ( p < -1.5093 ) = 0.07188
hence value of p0.05 < 0.07188,here we do not reject Ho
ANSWERS
---------------
null, Ho: =3.26
alternate, H1: <3.26
test statistic: -1.509
critical value: -1.708
decision: do not reject Ho
p-value: 0.07188

it reasonable to conclude the mean number of residents in the retirement community
household is less than 3.26 persons

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