# Homework 6

Homework 6

Questions 1 and 2) Suppose you are conducting consumer research for a bar. You want to study if male customers tip more if their bartender is female as opposed to male. You take collect a random sample of 12 men and ask them to come to a bar two nights in a row. On the first night they have a male bartender. On the second night they have a female bartender. You record the tips as percentages at the end of the night. You get the following data:

Subject Night 1 Night 2

1 18 21

2 15 22

3 25 35

4 16 30

5 15 19

6 20 25

7 10 30

8 20 36

9 10 22

10 20 33

11 20 26

12 12 30

Question 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 for male 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 coffee El Camino faculty drink during the school week. I randomly select 40 faculty members and ask them 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 that El Camino faculty drink during a school week. Write your interval as both a point estimate with a margin of error, and as an interval. Make sure to confirm all necessary conditions. Then write a sentence interpreting your confidence interval.

Question 4)

(a) Another faculty member has carried out a similar study and claims the average number of cups of 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 large

lecture with around 250 people) performs differently than his afternoon Calculus class (also a large lecture, but with around 350 people). On the next exam he randomly selects 12 students from

his morning class and 12 students from his afternoon class and records their scores. He gets the following data:

Morning Class: 56; 63; 64; 71; 74; 76; 78; 80; 83; 83; 87; 92

Afternoon Class: 55; 68; 75; 76; 78; 84; 86; 87; 88; 88; 90; 95

Question 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 difference between 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 their

intended _eld of study. I randomly select 20 students who have indicated that they want eventually major 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; 3:05

3:08; 3:09; 3:10; 3:13; 3:16; 3:24; 3:28; 3:35; 3:37; 3:46

Question 7) Carry out a hypothesis test at _ = :01 to test the claim that students in psychology have a higher than 3:0 GPA. Make sure to confirm all necessary conditions and interpret your conclusion in the context of the problem.

Question 8) Using the same data, construct a 95% confidence interval for the true average GPA of El Camino students intending on majoring in psychology. Make sure to write a sentence interpreting your interval.

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Questions 9 and 10) Suppose you work for a local private school with about 700 students. You want to run an advertisement that says, "Our students score better on the ACT!" To research this you look up the national average for the ACT and _nd it is 21 points with a standard deviation of

4:8 points. You then take a random sample of 32 of your own students and find out their average ACT 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 have set 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 and 10 on Night 2. Carry out the hypothesis test again. Did anything change? Would you trust these results? Why or why not?

Questions 1 and 2) Suppose you are conducting consumer research for a bar. You want to study if male customers tip more if their bartender is female as opposed to male. You take collect a random sample of 12 men and ask them to come to a bar two nights in a row. On the first night they have a male bartender. On the second night they have a female bartender. You record the tips as percentages at the end of the night. You get the following data:

Subject Night 1 Night 2

1 18 21

2 15 22

3 25 35

4 16 30

5 15 19

6 20 25

7 10 30

8 20 36

9 10 22

10 20 33

11 20 26

12 12 30

Question 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 for male 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 coffee El Camino faculty drink during the school week. I randomly select 40 faculty members and ask them 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 that El Camino faculty drink during a school week. Write your interval as both a point estimate with a margin of error, and as an interval. Make sure to confirm all necessary conditions. Then write a sentence interpreting your confidence interval.

Question 4)

(a) Another faculty member has carried out a similar study and claims the average number of cups of 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 large

lecture with around 250 people) performs differently than his afternoon Calculus class (also a large lecture, but with around 350 people). On the next exam he randomly selects 12 students from

his morning class and 12 students from his afternoon class and records their scores. He gets the following data:

Morning Class: 56; 63; 64; 71; 74; 76; 78; 80; 83; 83; 87; 92

Afternoon Class: 55; 68; 75; 76; 78; 84; 86; 87; 88; 88; 90; 95

Question 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 difference between 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 their

intended _eld of study. I randomly select 20 students who have indicated that they want eventually major 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; 3:05

3:08; 3:09; 3:10; 3:13; 3:16; 3:24; 3:28; 3:35; 3:37; 3:46

Question 7) Carry out a hypothesis test at _ = :01 to test the claim that students in psychology have a higher than 3:0 GPA. Make sure to confirm all necessary conditions and interpret your conclusion in the context of the problem.

Question 8) Using the same data, construct a 95% confidence interval for the true average GPA of El Camino students intending on majoring in psychology. Make sure to write a sentence interpreting your interval.

2

Questions 9 and 10) Suppose you work for a local private school with about 700 students. You want to run an advertisement that says, "Our students score better on the ACT!" To research this you look up the national average for the ACT and _nd it is 21 points with a standard deviation of

4:8 points. You then take a random sample of 32 of your own students and find out their average ACT 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 have set 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 and 10 on Night 2. Carry out the hypothesis test again. Did anything change? Would you trust these results? Why or why not?

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