State which hypothesis test best matches the scenario and justify your answer. 2 points each.
Choose and peform hypothesis tests for the following examples. Report your p-values!!.
[4 points] The number of yellow skittles is on average 8 per bag. Your bag has 11. Is this significantly different?
[4 points] You normally drink 8 oz of water with a standard deviation of 2 oz. Today you drank 12 oz. Is this significantly different?
[6 points] Ting says your cellphone bill will be about \$50 or lower if you switch. You switch and find your bills a are \$48, \$ 53, \$67, \$44. Was their claim correct?
[4 points] You are testing the efficacy of a drug that causes weight loss. You have 15 patients try the drug. Their weights in pounds before are [178,189,136,134,172,171,178,179,154,159,167,149,125,180,135] and after are [174,178,139,133,166,165,172,180,141,145,176,151,108,174,131]. Is the drug effective?
[6 points] You now add a control group which is given a placebo. Their before and after weights are [211,175,151,160,163,137,169,145,171,177,148,145,173,174,167] and [200,171,146,162,178,134,183,148,164,166,141,142,166,167,142]. Is your conclusion the same? Why or why not?
Solve the following problems using optimization. Report your answer in Markdown!. 4 Points each