According to the Census Bureau, 3.03 people reside in the typical American house

Question

According to the Census Bureau, 3.03 people reside in the typical American household. A sample of 18 households in Arizona retirement communities showed the mean number of residents per household was 2.87 residents. The standard deviation of this sample was 1.38 residents. At the .05 significance level, is it reasonable to conclude the mean number of residents in the retirement community household is less than 3.03 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.)

According to the Census Bureau, 3.03 people reside in the typical American household. A sample of 18 households in Arizona retirement communities showed the mean number of residents per household was 2.87 residents. The standard deviation of this sample was 1.38 residents. At the .05 significance level, is it reasonable to conclude the mean number of residents in the retirement community household is less than 3.03 persons?

Explanation / Answer

a) Null Hypothesis mu >= 3.03

    Alt Hypothesis mu < 3.03

b) sample size n = 18

degrees of freedom = n - 1 = 17

alpha = 0.05

critical value = -1.740

decision rule: reject null hypothesis if test stat < critical value (-1.740)

c) test stat t = (xbar - mu)/(stdev/sqrt(n))

                     = (2.87 - 3.03)/(1.38/sqrt(18))

                     = -0.492

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