# Homework 7

Homework 7

Directions: Homework must be written clearly and legibly. Make sure to give yourself adequate space for each question. Problems must be clearly numbered and the key parts of the problem itself should be restated. Make sure homeworks are stapled and have your name on top. All questions are worth 2 points.

3) The Cheapo company is getting ready to release their new headache reliever, Pain-B-Gone, for adults. However, according to FDA standards their drug can only cause severe side effects in 2% of the population. They are worried that their drug's side effects might be above this level.

They take a random sample of 800 adults and find that 24 of them experience severe side effects.

(a) Carry out a hypothesis test at a significance level of _ = :05 to test their claim. Check all the necessary conditions. Make sure to clearly state your conclusion in context of the problem at the end.

(b) What does a Type I error mean in context of this problem?

(c) What does a Type II error mean in context of this problem?

(d) Which type of error would be worse to make in this situation? Why?

4) Suppose you want to measure the current proportion of El Camino students that are playing Pokemon Go. To do this you take a random sample of 42 El Camino students and ask them if they are currently playing Pokemon Go. 28 of the people respond they are currently playing.

(a) Con_rm that it would not be appropriate to build a large sample confidence interval in this situation.

(b) Check the necessary conditions and build a +4 95% confidence interval for the true proportion of El Camino students playing Pokemon Go. Make sure to interpret your interval.

5) Question 23.26

6) Question 23.28

7) The mayor of a small town in New Mexico wants to know if his new policy of raising taxes to help support local feline charities has made him less popular. He took a random sample of 100 voters before enacting the new tax and found that 63 people said they approved of the job he was doing as mayor. After enacting the new tax he took a random sample of 200 voters and found that 112 people said they approved of the job he was doing as mayor.

(a) Carry out a hypothesis test at _ = :05 to see if there is evidence to support the claim that his new tax policy has lowered his approval rating. Make sure to confirm all necessary conditions for the test you choose. State your conclusion in the context of this situation.

(b) If the mayor was very worried about enacting a law that made him less popular would he retest at _ = :01 or _ = :10

8) Suppose that you want to study if El Camino students have different success rates on a basic math test and a basic grammar test. You select a random sample of 150 El Camino students and give each student both tests. You then get the following data about who passed and failed the exams.

Passed Math Failed Math

Passed Grammar 85 30

Failed Grammar 30 17

(a) Carry out a hypothesis test at _ = :05 to see if there was evidence that El Camino students performed differently on the two tests. Make sure to check all necessary conditions and state your conclusion in terms of the situation.

(b) Describe what it would mean to make a Type I error in this situation.

(c) Describe what it would mean to make a Type II error in this situation.

9) Question 25.30

10) Suppose that you work for a casino. You are tasked with regularly checking that the dice you use in your table games are not biased in any way. To do this you periodically randomly select a die that is being used and roll it 300 times. You get the following results:

Value Rolled 1 2 3 4 5 6

Number of Times Rolled 38 43 60 53 41 65

(a) Carry out a hypothesis test at _ = :05 to test the claim that this die is biased. Check all necessary conditions. Make sure to clearly state your conclusion in context of the problem at the

end.

(b) Describe what it would mean to make a Type I error in this situation.

(c) Describe what it would mean to make a Type II error in this situation.

Directions: Homework must be written clearly and legibly. Make sure to give yourself adequate space for each question. Problems must be clearly numbered and the key parts of the problem itself should be restated. Make sure homeworks are stapled and have your name on top. All questions are worth 2 points.

3) The Cheapo company is getting ready to release their new headache reliever, Pain-B-Gone, for adults. However, according to FDA standards their drug can only cause severe side effects in 2% of the population. They are worried that their drug's side effects might be above this level.

They take a random sample of 800 adults and find that 24 of them experience severe side effects.

(a) Carry out a hypothesis test at a significance level of _ = :05 to test their claim. Check all the necessary conditions. Make sure to clearly state your conclusion in context of the problem at the end.

(b) What does a Type I error mean in context of this problem?

(c) What does a Type II error mean in context of this problem?

(d) Which type of error would be worse to make in this situation? Why?

4) Suppose you want to measure the current proportion of El Camino students that are playing Pokemon Go. To do this you take a random sample of 42 El Camino students and ask them if they are currently playing Pokemon Go. 28 of the people respond they are currently playing.

(a) Con_rm that it would not be appropriate to build a large sample confidence interval in this situation.

(b) Check the necessary conditions and build a +4 95% confidence interval for the true proportion of El Camino students playing Pokemon Go. Make sure to interpret your interval.

5) Question 23.26

6) Question 23.28

7) The mayor of a small town in New Mexico wants to know if his new policy of raising taxes to help support local feline charities has made him less popular. He took a random sample of 100 voters before enacting the new tax and found that 63 people said they approved of the job he was doing as mayor. After enacting the new tax he took a random sample of 200 voters and found that 112 people said they approved of the job he was doing as mayor.

(a) Carry out a hypothesis test at _ = :05 to see if there is evidence to support the claim that his new tax policy has lowered his approval rating. Make sure to confirm all necessary conditions for the test you choose. State your conclusion in the context of this situation.

(b) If the mayor was very worried about enacting a law that made him less popular would he retest at _ = :01 or _ = :10

8) Suppose that you want to study if El Camino students have different success rates on a basic math test and a basic grammar test. You select a random sample of 150 El Camino students and give each student both tests. You then get the following data about who passed and failed the exams.

Passed Math Failed Math

Passed Grammar 85 30

Failed Grammar 30 17

(a) Carry out a hypothesis test at _ = :05 to see if there was evidence that El Camino students performed differently on the two tests. Make sure to check all necessary conditions and state your conclusion in terms of the situation.

(b) Describe what it would mean to make a Type I error in this situation.

(c) Describe what it would mean to make a Type II error in this situation.

9) Question 25.30

10) Suppose that you work for a casino. You are tasked with regularly checking that the dice you use in your table games are not biased in any way. To do this you periodically randomly select a die that is being used and roll it 300 times. You get the following results:

Value Rolled 1 2 3 4 5 6

Number of Times Rolled 38 43 60 53 41 65

(a) Carry out a hypothesis test at _ = :05 to test the claim that this die is biased. Check all necessary conditions. Make sure to clearly state your conclusion in context of the problem at the

end.

(b) Describe what it would mean to make a Type I error in this situation.

(c) Describe what it would mean to make a Type II error in this situation.

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