Question

According to the Census Bureau, 3.34 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 2.70 residents. The standard deviation of this sample was 1.17 residents. At the 10 significance level, is it reasonable to conclude the mean number of residents in the retirement community household is less than 3.34 persons? a. State the null hypothesis and the alternate hypothesis. (Round your answer to 2 decimal places.) ek H με H1:u nces 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 HO if t

Answer 1

Part a)

To Test :-
H0 :- µ <= 3.34
H1 :- µ < 3.34

Part b)

Reject null hypothesis if t < -t(α, n-1)
Critical value t(α, n-1) = t(0.1 , 26-1) = 1.316
t < - 1.316

Part c)

Test Statistic :-
t = ( X̅ - µ ) / (S / √(n) )
t = ( 2.7 - 3.34 ) / ( 1.17 / √(26) )
t = -2.789

Part d)

Test Criteria :-
Reject null hypothesis if t < -t(α, n-1)
Critical value t(α, n-1) = t(0.1 , 26-1) = 1.316
t < - t(α, n-1) = -2.7892 < - 1.316
Result :- Reject null hypothesis

HO. Mean number of residents less than 3.34 persons

Reject H0, mean number of residents is less than 3.34 persons.