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: μ ≥
H1: μ <

(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 not necessarilyis necessarily less than 3.26 persons.

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is ,

H₀ :   = 3.26

H_a : < 3.26

n = 26

df = 25

Reject H0 . If t < -1.708

Test statistic = t

= ( - ) / s / n

= (2.89 - 3.26 ) / 1.25 / 26

= -1.509

Test statistic < critical value

Fail to reject the null hypothesis .

There is not sufficient evidence to conclude that the mean number of residents in the retirement community household is less than 3.26 persons .