Question

According to the Census Bureau, 3.13 people reside in the typical American household. A sample of 25

households in Arizona retirement communities showed the mean number of residents per household

was 2.86 residents. The standard deviation of this sample was 1.20 residents. At the .05 significance

level, is it reasonable to conclude the mean number of residents in the retirement community household is less than 3.13 persons? Use the 5-step process; show your work.

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is ,

H₀ :   = 3.13

H_a : < 3.13

Test statistic = t

= ( - ) / s / n

= (2.86 - 3.13) / 1.20 / 25

= -1.125

n = 25

df = 25 - 1 = 24

P-value = 0.1359

= 0.05

P-value >

Fail to reject the null hypothesis .

There is sufficient evidence to conclude the mean number of residents in the retirement community household is

less than 3.13 persons .