According to the Census Bureau 3 33 people reside in the typ

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

Solution

(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.