Suppose you are conducting consumer research for a bar. You want to study ifmale customers tip more if their bartender is female as opposed to male. You take collect a randomsample of 12 men and ask them to come to a bar two nights in a row. On the first night theyhave a male bartender. On the second night they have a female bartender. You record the tips aspercentages at the end of the night. You get the following data:Subject Night 1 Night 21 18 212 15 223 25 354 16 305 15 196 20 257 10 308 20 369 10 2210 20 3311 20 2612 12 30Question 1) Carry out a hypothesis test at _ = :01 Make sure to confirm all the necessary conditions.State your conclusion in context of the situation.Question 2) Construct a 95% confidence interval for the difference between tip percentages formale and female bartenders with male customers. Write a sentence explaining your interval.Questions 3 and 4) Suppose I am interested in studying the average number of cups of coffeeEl Camino faculty drink during the school week. I randomly select 40 faculty members and askthem to record how many cups of coffee they drink during the week. At the end of the week I calculate that they drank an average of 7:3 cups of coffee with a standard deviation of 4:8 cups of coffee.Question 3) Construct a 98% confidence interval for the average number of cups of coffee thatEl Camino faculty drink during a school week. Write your interval as both a point estimate witha margin of error, and as an interval. Make sure to confirm all necessary conditions. Then write asentence interpreting your confidence interval.Question 4)(a) Another faculty member has carried out a similar study and claims the average number of cupsof coffee drank in a week is 5. Would you consider this likely, unlikely, or impossible? Why?(b) Would you feel comfortable using your interval to estimate the average number of cups of coffee that El Camino students drink during a school week? Why or why not?Questions 5 and 6) Suppose a professor wants to know if his morning Calculus class (a largelecture with around 250 people) performs differently than his afternoon Calculus class (also a largelecture, but with around 350 people). On the next exam he randomly selects 12 students fromhis morning class and 12 students from his afternoon class and records their scores. He gets thefollowing data:Morning Class: 56; 63; 64; 71; 74; 76; 78; 80; 83; 83; 87; 92Afternoon Class: 55; 68; 75; 76; 78; 84; 86; 87; 88; 88; 90; 95Question 5) Carry out an appropriate hypothesis test at _ = :05 to test the professor’s claim.Make sure to check all necessary conditions. State your conclusion in context of the problem.Question 6) Using the same data, construct a 95% confidence interval for the average differencebetween the morning class and the afternoon class. Make sure to interpret your interval.Questions 7 and 8) Suppose I want to study the GPA’s of El Camino students based on theirintended _eld of study. I randomly select 20 students who have indicated that they want eventuallymajor in psychology. Their GPA’s are listed in increasing order below.2:76; 2:84; 2:88; 2:93; 2:94; 2:97; 2:98; 3:02; 3:05; 3:053:08; 3:09; 3:10; 3:13; 3:16; 3:24; 3:28; 3:35; 3:37; 3:46Question 7) Carry out a hypothesis test at _ = :01 to test the claim that students in psychologyhave a higher than 3:0 GPA. Make sure to confirm all necessary conditions and interpret yourconclusion in the context of the problem.Question 8) Using the same data, construct a 95% confidence interval for the true average GPA ofEl Camino students intending on majoring in psychology. Make sure to write a sentence interpretingyour interval.2Questions 9 and 10) Suppose you work for a local private school with about 700 students. Youwant to run an advertisement that says, “Our students score better on the ACT!” To research thisyou look up the national average for the ACT and _nd it is 21 points with a standard deviation of4:8 points. You then take a random sample of 32 of your own students and find out their averageACT score was 23:2.Question 9) Carry out a hypothesis test at _ = :05 to see if you can run your advertisement.Make sure to check all necessary conditions and interpret your conclusion in context of this situation.Question 10)(a) If you were worried about missing the opportunity to run your advertisement should you haveset your _ to :01 or :1?(b) If you were worried about running a false advertisement should you have set your _ to :01 or:1?EXTRA CREDIT QUESTION:Look back at Question 1. Suppose that Subject 7 was accidentally recorded as 30 on Night 1 and10 on Night 2. Carry out the hypothesis test again. Did anything change? Would you trust theseresults? Why or why not?