According to the Census Bureau, 3.14 people reside in the typical American house
ID: 3383172 • Letter: A
Question
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.)
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?
Explanation / Answer
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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