Justin introduces two examples in order to explain the concept of conducting a formal hypothesis testing for μ when σ is known. The questions are provided below with time references.
One-tailed example (0:26):
The manager of a department store is thinking about establishing a new billing system for the store’s credit customers. 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 $74. The manager knows that the accounts are normally distributed with a standard deviation of $30. Is there enough evidence at the 5% level of significance to conclude that the new system will be cost effective?
1.State Null and Alternate Hypotheses (1:40)
2.Calculate test statistic (4:13)
3.Consider decision rule (5:12)
3a. Calculate p-value (6:55)
4. State rejection decision (8:23)
5. Conclusion (9:28)
Two tailed example (9:58):
A new toll road is being built and financed on the expectation that 8,500 cars will use it per day. In the first 30 days of its operation, a daily average of 8,120 cars were found to have used the toll road. Using the 1% level of significance, test whether the expectation was incorrect. (Assume that the distribution of daily road users is normally distributed with a standard devation of 950)
1.State Null and Alternate Hypotheses (11:06)
2.Calculate test statistic (11:46)
3.Consider decision rule (11:58)
3a. Calculate p-value (13:28)
4. State rejection decision (14:21)
5. Conclusion (14:40)