According to the Census Bureau, 3.21 people reside in the typical American house

Question

According to the Census Bureau, 3.21 people reside in the typical American household. A sample of 25 households in Arizona retirement communities showed the mean number of residents per household was 2.74 residents. The standard deviation of this sample was 1.35 residents. At the .05 significance level, is it reasonable to conclude the mean number of residents in the retirement community household is less than 3.21 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 3.21 persons?

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According to the Census Bureau, 3.21 people reside in the typical American household. A sample of 25 households in Arizona retirement communities showed the mean number of residents per household was 2.74 residents. The standard deviation of this sample was 1.35 residents. At the .05 significance level, is it reasonable to conclude the mean number of residents in the retirement community household is less than 3.21 persons?

Explanation / Answer

(a) Ho: 3.21 versus Ha: < 3.21

(b)

= 0.05

Degrees of freedom = 25 - 1 = 24

Critical t- score = -1.711

Reject Ho if t < -1.711

(c)

SE = s/n = 1.35/25 = 0.27

t = (x-bar - )/SE = (2.74 - 3.21)/0.27 = -1.741

(d) Since -1.740740741 < -1.710882067 we reject Ho and accept Ha

It is reasonable to conclude the mean number of residents in the retirement community household is less than 3.21 persons.

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