BA 275 Quantitative Business Methods Agenda Multiple Linear Regression: Dummy Variables Statistical Inference: Population Proportion Confidence Interval Estimation Hypothesis Testing

Using Dummy Variables

Dummy Variable for LOCATION

Fitted Model

Questions Write down the fitted model. Is the assumed model reliable? Why? What is the value of R2? the adjusted R2? To select a model, why do we prefer adj-R2 to R2? Predict the amount of money withdrawn from a neighborhood in which the median value of homes is $200,000 for an ATM that is located in a shopping center. If the median value of homes increases by $2,000, then the amount of money withdrawn from an ATM located in a shopping center is expected to increase by . If the median value of homes is $200,000, then the amount of money withdrawn from an ATM located in a shopping center is ???; and the amount of money withdrawn from an ATM located outside a shopping center is ???. What is the difference?

Two Lines with the Same Slopes but Different Intercepts

Two Lines with Different Intercepts and Slopes

Analyzing Categorical Data Do you own an iPod? ___Yes ___No Do you own a XBoX? ___Yes ___No Which of the following 4 soft drinks gives you the highest satisfaction? Type A ___ Type B ___ Type C ___ Type D ___ Your gender: ____Male ____ Female Your nationality: _____

Central Limit Theorem In the case of sample mean In the case of sample proportion

Formulas for Proportion 100(1-a)% confidence interval estimator Hypothesis testing H0: p = p0

Example 1 A sample of 35 student information sheets shows that 9 intend to concentrate in Finance. Give a 99% confidence interval for the proportion of students in the population that intend to concentrate in Finance.

Margin of Error (m) Margin of Error (how good is your point estimate?)

Example 2 A marketing manager for a start-up firm in Michigan wishes to discover the proportion of teenagers in Japan who own an iPod. If the manager wants a confidence interval of width 0.1, how many teenagers must be sampled? Use a conservative estimate of p. Assume that the confidence level is to be 95%.

Accuracy Gained by Increasing the Sample Size Margin of Error (B) Sample Size (n) 7% 196 6% 266 5% 384 4% 600 3% 1037 2% 2401 1% 9604

Hypothesis Testing 4 out of 5 dentists recommend Oral-B. Scenario 1: “Hmm, I thought it was higher.” Scenario 2: “No, it cannot be. It should be lower.” Scenario 3: “Really? I don’t think so.”

Example 3 Three politicians are attempting to win the Democratic nomination for senator. The result of a survey of 1000 Democrats is summarized below. Do we have enough evidence to indicate that Candidate A will receive more than 50% of the vote? Assume a = 5%. (use the rejection region and the p-value approaches.) Candidate A 550 Candidate B 300 Candidate C 150

Example 4 In recent years over 70% of first-year college students responding to a national survey have identified “being well-off financially” as an important personal goal. A state university finds that 153 of a random sample of 200 of its first-year students say that this goal is important. Do we have evidence to support that more than 70% of first-year students would identify being well-off as an important personal goal? (use the rejection region and the p-value approaches.) Assume a = 5%.

Example 5 A financial analyst wanted to determine the mean annual return on mutual funds. In a random sample of 15 returns she found a sample mean of 12.9% with a (sample) standard deviation 3%. Is there evidence to claim that the mean annual return on mutual funds is greater than 12%? Assume a = 5%.

Answer Key to Examples 1 – 3

Answer Key to Examples 4 – 5