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# PhoneEx Statistical Analysis

1.Provide an example of an experiment or data that has two factors. Provide details (what is being measured and the number of levels) of the levels for factor A and factor B.

2. PhoneEx provides call center services for many different companies. A large increase in its business has made it necessary to establish a new call center. Four cities are being considered - Little Rock, Wichita, Tulsa and Memphis. The new center will employ approximately 1500 workers and PhoneEx will transfer 75 people from its Omaha center to the new location. Once concern in the choice of where to locate the new center is the cost of housing for the new employees that will be moving there. To help determine whether significant housing cost differences exist across the competing sites, PhoneEx has asked a real estate broker in each city to randomly select a list of 33 homes between 5 and 15 years old and ranging in size between 1975 and 2235 square feet. The prices ( in dollars) that were recorded for each city are contained in the file called PhoneEx.

a) At the 0.05 level of significance, is there evidence to conclude that the average price of houses between 5 and 15 years old and ranging in size between 1975 and 2235 square feet is not the same in the house cities? Use the p-value approach.

b) At the 0-05 level of significance, is there a difference in average housing price between Wichita and Little Rock? Between Little Rock and Tulsa? Between Tulsa and Memphis?

c) Determine the sample size required to estimate the average housing price in Wichita to within \$500 with a 95% confidence level. Assume that required parameters estimates are sufficient for this calculation.

#### Solution Preview

1.
Suppose we want to perform an analysis as to whether age (in months) affects the number of words known in little children. For this we collect the data of age and number of words known in a number of children. In this analysis, Factor A represents the independent variable 'age' of the children and Factor B represents the dependent variable 'number of words known'. Both Factor A and Factor B are measured using ratio scale of measurement.

2.
a)
Null and Alternate Hypothesis:
Null Hypothesis: The average price of houses between 5 and 15 years old and ranging in size between 1975 and 2235 square feet is same in all the four cities. .

Alternate Hypothesis: At least one of the cities has a significantly different price of houses between 5 and 15 years old and ranging in size between 1975 and 2235 square feet.

Analysis Plan: We shall use ANOVA to test the given hypothesis. The chosen level of significance for the given hypothesis test is 0.05.

Calculation of ...

\$2.19