According to the Census Bureau, 3 33 people reside in the typical American house

Question

According to the Census Bureau, 3 33 people reside in the typical American household. A sample of 21 households in Arizona retirement communities showed the mean number of residents per household was 2 86 residents The standard deviation of this sample was 1.32 residents. At the 10 significance level, is it reasonable to conclude the mean number of residents in the retirement commune 1 household is less than 3.33 person? State the null hypothesis and the alternate hypothesis. State the decision rule for 10 significance level Compute the value of the test statistic

Explanation / Answer

(a) Ho: mu>=3.33

H1: mu<3.33

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(b) The degree of freedom =n-1=21-1=20

It is a left-tailed test.

Given a=0.1, the critical value is t(0.1, df=20) =-1.325 (from student t table)

Reject Ho if t<-1.325

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(c) The test statistic is

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

=(2.86-3.33)/(1.32/sqrt(21))

=-1.632

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(d) Reject Ho.

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