1. In a bottling process, a manufacturer will lose money if the bottles contain either more or, less than is claimed on the label. The quality manager of a plant is interested in testing whether the mean ounces of catsup per family size bottle differ from the label by amount of 20 ounces. A sample of 9 bottles yields a mean fill of 19.7 ounces with a standard deviation of 0.3 ounces. Does the sample evidence indicate that the catsup-dispensing machines need adjustment at a 98% confidence?
2. A secretarial school that specializes in word processing wants to attract new students by touting its graduates' highly successful job placement records. The school's enrollment officer has decided to get the word out that its graduate average at least $10.50 per hour in their first job after graduation. The problem is, he/she has no evidence to back up this claim. With advertising brochures about to go to the printer, the enrollment officer suddenly worried that someone will challenge the claim and expose him/her. To keep the peace of mind, he/she samples 36 recent graduates and finds that the average starting salary is $10.25 with a standard deviation of $1.25. Does the sample data support the claim at a 99% confidence?
This solution shows step by step calculations and explanations for two hypothesis tests (t-tests).