BA 275 Quantitative Business Methods

1. BA 275 Quantitative Business Methods Agenda • Statistical Inference – Hypothesis Testing • Tests for a Population Mean • Examples • Quiz #5

2. Statistical Inference: Hypothesis Testing Example: s = 10,000 n = 100 Is “m > 22,000”? Population Research Question: Is a claim about the parameter value supported? Example: “m > 22,000”? Sample of size n Tool (i.e., formula): Z or T score

3. Before collecting data After collecting data Elements of a Test • Hypotheses • Null Hypothesis H0 • Alternative Hypothesis Ha • Test Statistic • Decision Rule (Rejection Region) • Evidence (actual observed test statistic) • Conclusion • Reject H0 if the evidence falls in the R.R. • Do not reject H0 if the evidence falls outside the R.R.

4. 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?

5. Example 1 (p.19) • 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?

6. Type I and II Errors Chance of making Type I error = P( Type I error ) = a Chance of making Type II error = P( Type II error ) = b

7. Example 2 (p. 19) • The manager of a department store is thinking about establishing a new billing system for the store’s credit customers. After a thorough financial analysis, she determines that the new system will be cost-effective only if the mean monthly account is greater than $70. A random sample of 200 monthly accounts Is drawn, for which the sample mean account is $76 with a standard deviation of $30. Is there enough evidence at the 5% significance level to conclude that the new system will be cost-effective? • What if the sample mean is $68? $74?

8. Example • How much time do executives spend each day reading and sending e-mail? A survey of 162 executives was conducted and the mean time (in minutes) was 63.6975 minutes. • Assume that the std is 18.9403 (Does it matter if this std is a population or a sample std?). Can we infer that the mean amount of time spent by all executives reading and sending e-mail exceeds 60 minutes? • Assume 5% significance level.

9. Example • How much time do executives spend each day reading and sending e-mail? A survey of 162 executives was conducted and the mean time (in minutes) was 63.6975 minutes. • Assume that the std is 18.9403. Can we infer that the mean amount of time spent by all executives reading and sending e-mail is different from 60 minutes? • Assume 5% significance level.

10. Example • How much time do executives spend each day reading and sending e-mail? A survey of 162 executives was conducted and the mean time (in minutes) was 63.6975 minutes with a standard deviation of 18.9403. • At 5% significance level, we concluded that the mean amount of time exceeds 60 minutes. • By how much?

11. Example • How much time do executives spend each day reading and sending e-mail? A survey of 12 executives was conducted and the mean time (in minutes) was 63.6975 minutes. • Assume that the sample std is 18.9403. Can we infer that the mean amount of time spent by all executives reading and sending e-mail exceeds 60 minutes? • Assume 5% significance level.