Question

According to the Census Bureau, 3.34 people reside in the typical American household. A sample of 27 households in Arizona retirement communities showed the mean number of residents per household was 2.86 residents. The standard deviation of this sample was 1.13 residents. At the .05 significance level, is it reasonable to conclude the mean number of residents in the retirement community household is less than 3.34 persons? a. State the null hypothesis and the alternate hypothesis. (Round your answer to 2 decimal places.) H0: ? ? H1: ? < b. State the decision rule for .05 significance level. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.) Reject H0 if t < c. Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.) Value of the test statistic d. Is it reasonable to conclude the mean number of residents in the retirement community household is less than 3.34 persons? H0. Mean number of residents less than 3.34 persons.

Answer 1

As we are trying to test whether the mean is less than 3.34, therefore the null and the alternate hypothesis here are given as:

b) For n - 1 = 26 degrees of freedom, we get from the t distribution tables that:

P( t₂₆ <-1.706 ) = 0.05

Therefore the decision rule here is Reject H₀if Z < -1.706

c) The test statistic here is computed as:

Therefore -2.207 is the test statistic value here.

d) As the test statistic value here is -2.207 < -1.706, therefore it lies in the rejection region, and we can reject the null hypothesis here and conclude that we have sufficient evidence that the mean is lower.