Analysis Of Variance
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Analysis of Variance
Based upon the information found in the cost analysis last week, Adam found out that mean price of the offices are quite similar regardless of the location. Therefore, Adam assume that finding good office space for the real estate brokerage can be based solely upon choice without too much consideration location. Adam then decided to collect the sample office prices from San Francisco area to find out whether there is a difference in mean price if office space in three different locations: San Francisco, Sacramento, and outlying areas of Sacramento.
Adam will formulate a hypothesis statement and perform the five-step hypothesis test on the data he collected.
Step 1: State the null hypothesis and the alternate hypothesis. The null hypothesis is that the mean prices are the same for the three locations.
H0: Ñ”Ð1 = Ñ”Ð2 = Ñ”Ð3
The alternate hypothesis is that the mean prices are not all the same for the three locations.
H0: The mean prices are not all equal.
We can also think of the alternate hypothesis as ÐŽ§at least two mean prices are not equal.ÐŽÐ
If the null hypothesis is not rejected, we conclude that there is no difference in the mean prices in all the location. If H0 is rejected, we conclude that there is a difference in at least one pair of mean prices.
Step 2: Select the level of significance. We selected the .01 significance level.
Step 3: Determine the test statistic. The test statistic follows the F distribution.
Step 4: Formulate the decision rule. Reject H0 and Accept H1 if Fcal is > Fcrit
Step 5: Select the sample, perform the calculations, and make a decision.
Sacramento
surrounding area of
Sacramento
Fransisco