Sketch the density curve of the sampling distribution
The Census Bureau reports that households spend an average of 31% of their total spending on housing. A homebuilders association in Cleveland believes that this average is lower in their area. They interview a sample of 40 households in the Cleveland metropolitan area to learn what percent of their spending goes toward housing. Take mean Mu to be the mean percent of spending devoted to housing among all Cleveland households. We want to test the hypotheses Ho: mean = 31%
Ha: mean < 31%
Assume that the population standard deviation is 9.6%.
a) What is the sampling distribution of the mean percent x-bar that the sample spends on housing if the null hypotheseis it true? Sketch the density curve of the sampling distribution. Be sure to locate mean and standard deviationn correctly.
B) Suppose that the study finds x-bare = 30.2% for the 40 households in the sample. Mark this point on the axis in your sketch. Then suppose that the study result is x-bar = 27.6%. Mark this point on your sketch. Referring to your sketch, explain in simple housing is less than 31%, whereas the other result is not.
C) Shade the area under the curve that gives the P-value for the result x-bar 30.2%. (Note that we are looking for evidence tht spending is less than the null hypothesis states.) Now shade differently the area under the curve that represents the P-value for x-bar = 27.6%. Find these two P-values.