2. Example Suppose we want to prove that the mean commute time for people in Lexington to get to work is less than 20 minutes. A random sample of 125 people yield a sample mean of 17.8 minutes. Assume the population standard deviation is 12.9. State the hypotheses Calculate the test statistic Identify the p-value Make your decision using 0.01 as the level of significance Interpret the results

3. Example Suppose we want to prove that the mean commute time for people in Lexington to get to work is less than 20 minutes. A random sample of 125 people yield a sample mean of 17.8 minutes. Assume the population standard deviation is 12.9. How would changing the level of significance to 0.05 affect the hypothesis test? How would increasing the sample size affect the hypothesis test? How would a larger population standard deviation effect the hypothesis test?

4. Example A system manager at a large corporation believes more than 80% of all email received at the corporation is spam. A simple random of 800 emails received finds that 688 are spam. Test the managers claim. State the hypotheses Calculate the test statistic Identify the p-value Make your decision using 0.05 as the level of significance Interpret the results