According to the Census Bureau, 3.29 people reside in the typical American house

Question

According to the Census Bureau, 3.29 people reside in the typical American household. A sample of 16 households in Arizona retirement communities showed the mean number of residents per household was 2.76 residents. The standard deviation of this sample was 1.29 residents. At the .05 significance level, is it reasonable to conclude the mean number of residents in the retirement community household is less than 3.29 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 3.29 persons?

According to the Census Bureau, 3.29 people reside in the typical American household. A sample of 16 households in Arizona retirement communities showed the mean number of residents per household was 2.76 residents. The standard deviation of this sample was 1.29 residents. At the .05 significance level, is it reasonable to conclude the mean number of residents in the retirement community household is less than 3.29 persons?

Explanation / Answer

a)

Formulating the null and alternative hypotheses,              
              
Ho:   u   >=   3.29  
Ha:    u   <   3.29   [ANSWER]

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b)
              
As we can see, this is a    left   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    15          
tcrit =    -   1.753050356      

Thus, Reject Ho when t < -1.753. [ANSWER]

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c)
              
Getting the test statistic, as              
              
X = sample mean =    2.76          
uo = hypothesized mean =    3.29          
n = sample size =    16          
s = standard deviation =    1.29          
              
Thus, t = (X - uo) * sqrt(n) / s =    -1.643 [ANSWER]

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d)          
              
As |t| < 1.753, we   FAIL TO REJECT THE NULL HYPOTHESIS.   [ANSWER]

Mean number of residents IS NOT necessarily less than 3.29 persons.      
              

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