1 BA 275 Quantitative Business Methods Hypothesis Testing using the p-Value Statistical Inference on Two Populations Quiz #6 Agenda.

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1 BA 275 Quantitative Business Methods Hypothesis Testing using the p-Value Statistical Inference on Two Populations Quiz #6 Agenda

2 Midterm Examination #2 Wednesday, 3/1/06 in class. Closed books/notes/packet/friends exam, but I will provide you The normal and the T tables The formulas on pp. 13, 14, and 17. Need a good night sleep and a calculator that WORKS! Topics: The Normal Distribution and the Central Limit Theorem Confidence Interval Estimation, Margin of Error, Sample Size Determination Hypothesis Testing, the p-value approach CyberStats: B-11, B-12, C-1, C-2, C-3, C-4, C-6, C-7, C-8.

3 Review Example A financial analyst wanted to determine the mean annual return on mutual funds. In a random sample of 15 returns she found a mean of 12.9% with a standard deviation 3%. Q1. Is there evidence to claim that the mean annual return on mutual funds is greater than 12%? Q2. If so, by how much?

4 Review Example 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. Q1. Do we have evidence to support that more than 70% of first-year students would identify being well- off as an important personal goal? Q2. Estimate with 95% confidence the population proportion.

5 Review Example A survey of 100 retailers revealed that the mean after-tax profit was $75,000. If we assume that the population standard deviation is $20,000. Q1. Is there evidence to claim that the mean after-tax profit exceeded $70,000? Q2. Estimate the true mean after-tax profit using a 95% confidence interval.

6 The p-Value Approach (p.20) (Cyberstats) The p-value is the probability, under the assumption that H 0 is true, of obtaining a test statistic as or more extreme than the one actually obtained from the data. (The packet) The p-value is the smallest value of  that would lead to rejection of H 0. (Ping’s) What is the chance of making a type I error if H 0 is rejected with the given sample? Small p-valve => small chance of making type I error => reject H 0

7 Example A bank has set up a customer service goal that the mean waiting time for its customers will be less than 2 minutes. The bank randomly samples 30 customers and finds that the sample mean is 100 seconds. Assuming that the sample is from a normal distribution and the standard deviation is 28 seconds, can the bank safely conclude that the population mean waiting time is less than 2 minutes? Find the p-value.

8 Example A bank has set up a customer service goal that the mean waiting time for its customers will be less than 2 minutes. The bank randomly samples 30 customers and finds that the sample mean is 112 seconds. Assuming that the sample is from a normal distribution and the standard deviation is 28 seconds, can the bank safely conclude that the population mean waiting time is less than 2 minutes? Find the p-value.

9 Example A survey of 100 retailers revealed that the mean after-tax profit was $75,000. If we assume that the population standard deviation is $20,000. Is there evidence to claim that the mean after- tax profit exceeded $70,000? Use the p-value approach.

10 Two-Sample Inference on  1 –  2 Population #1Population #2 Sample #2Sample #1

11 Two-Sample Inference on p 1 – p 2 Population #1Population #2 Sample #2Sample #1

12 Example (p.21) U.S. SalesJapan Sales Sample size3050 Sample mean$14,545$15,243 Sample Std.$ 1,989$ 1,842 Part 1. Q1. Do we have enough evidence to claim that the auto retail price in Japan is higher? Q2. If so, by how much? Part 2. Q1. Do we have enough evidence to claim that the auto retail price in Japan is $500 higher? Q2. If so, by how much?