According to the Census Bureau 320 people reside in the typi

According to the Census Bureau, 3.20 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 2.86 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 3.20 persons?

State the decision rule for .05 significance level. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)

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

Is it reasonable to conclude the mean number of residents in the retirement community household is less than 3.20 persons?

Solution

(a) Ho: mu=3.20

Ha: mu<3.20

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(b) The degree of freedom =n-1=26-1=25

Given a=0.05, the critical value is t(0.05, df=25) =-1.708 (from student t table)

  Reject H₀ if t < -1.708

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(c) test statistic is

t=(xbar-mu)/(s/vn)

=(2.86-3.2)/(1.2/sqrt(26))

=-1.445

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(d)Fail to reject H₀. Mean number of residents is not necessarily less than 3.20 persons.