According to the Census Bureau 314 people reside in the typi

According to the Census Bureau, 3.14 people reside in the typical American household. A sample of 20 households in Arizona retirement communities showed the mean number of residents per household was 2.82 residents. The standard deviation of this sample was 1.11 residents. At the .10 significance level, is it reasonable to conclude the mean number of residents in the retirement community household is less than 3.14 persons?

State the decision rule for .10 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.)

Solution

a)

Formulating the null and alternative hypotheses,              
              
Ho:   u   >=   3.14  
Ha:    u   <   3.14   [ANSWER]

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b)

              
As we can see, this is a    left   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    19          
tcrit =    -   1.327728209      

Thus, the decision rule is

Reject Ho if t < -1.328. [ANSWER]

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c)
              
Getting the test statistic, as              
              
X = sample mean =    2.82          
uo = hypothesized mean =    3.14          
n = sample size =    20          
s = standard deviation =    1.11          
              
Thus, t = (X - uo) * sqrt(n) / s =    -1.289 [ANSWER]

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