Question

According to the Census Bureau, 3.39 people reside in the typical American household. A sample of 26 households in Arizona retirement communities showed the mean number of residents per household was 2.73 residents. The standard deviation of this sample was 1.22 residents. At the .10 significance level, is it reasonable to conclude the mean number of residents in the retirement community household is less than 3.39 persons?

1. ate the null hypothesis and the alternate hypothesis. (Round your answer to 2 decimal places.)

2. State the decision rule for .10 significance level. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)

3. Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)

4. Is it reasonable to conclude the mean number of residents in the retirement community household is less than 3.39 persons?

Answer 1

a)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 3.39
Alternative Hypothesis, Ha: μ < 3.39

b)

Rejection Region
This is left tailed test, for α = 0.1 and df = 25
Critical value of t is -1.316.
Hence reject H0 if t < -1.316

c)

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (2.73 - 3.39)/(1.22/sqrt(26))
t = -2.758

d)

yes, it is reasonable to conclude the mean number of residents in the retirement community household is less than 3.39 persons