Question 1 - A principle at a certain high school claims that the students in her school are above average in SAT. She collects a random sample of 50 students and given an SAT test that provided with a mean score of 541. Is there sufficient evidence statistically to support the principal’s claim? The mean population SAT score is 500 with a standard deviation of 100. SAT scores are normally distributed. Please show all the steps involved in a hypothesis testing including proper statistical symbols, formula used, and report/interpret results in complete sentences. Question 2 (13 points):
Blood nicotine levels in regular cigarette smokers have a mean of 100 mg with a standard deviation of 15 mg. A smoking researcher investigates whether e-cigarettes have positive or negative effect on blood nicotine levels. He gave e-cigarettes to a random sample of 30 smokers and found a mean nicotine level of 140 mg. Test the hypothesis that e-cigarettes had an effect. Please show all the steps involved in a hypothesis testing including proper statistical symbols, formula used, and report/interpret results in complete sentences.

Question 3 (13 points):
Blood nicotine levels in regular cigarette smokers have a mean of 100 mg but standard deviation is unknown. A smoking researcher investigates whether e-cigarettes have positive or negative effect on blood nicotine levels. He gave e-cigarettes to a random sample of 30 smokers and found a mean nicotine level of 140 mg with a standard deviation of 20 mg. Test the hypothesis that e-cigarettes had an effect. Please show all the steps involved in a hypothesis testing including proper statistical symbols, formula used, and report/interpret results in complete sentences.