1. Mary claims to be able to hypnotically cause her clients to perform significantly higher on the SAT. The national mean is 1200 with a standard deviation of 100. Under strictly controlled testing, a random sample of 200 of her clients revealed a mean score of 1210. Does this data support her claim. Show all steps.
2. The Greasy Spoon Restaurant has an automatic hamburger patty machine, a new addition to their kitchen intended to save time, effort and money. The manufacture had designed the machine so each patty weighs 4 ounces. To test the equipment, 32 hamburgers were prepared and found to have a mean weight of 4.2 ounces and a standard deviation of 0.6 ounces. Test at alpha=0.1, the restaurant's claim that the machine always dispenses more than 4 ounces and so they should raise the burger prices.
The solution gives complete steps of one sample student t test for comparing the mean with a standard value. The interpretations of the results are also given.