Suggested Exercises 4
Math 150, FALL 2018
Directions: In this document you will find eleven questions I have written for your practice. I would recommend you attempt as many of these as possible to make sure you’re familiar with not only the concepts presented in each section but also the types of questions that are associated with these topics.If you have any questions send me an email, ask during class, or see me during office hours.
Question 1) A drug 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 α = .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?
Question 2) Suppose you’re interested in studying shopping trends in America. You know ac-cording to reports from last year 31% of American adults went shopping in stores on Black Friday. You want to know if that percentage has changed. To study this you take a random sample of 300 American adults this year and find out that 82 of them went shopping on Black Friday this year. (a) Carry out a hypothesis test at α = .05 to see if there is evidence that the percentage of American adults who go Black Friday shopping has changed from last year.
(b) If you were worried about falsely concluding that the percetange of American adults who go Black Friday has changed would you retest at α=.01 or .10?
Question 3) Suppose you work for a large college (around 30000 students) and your job is to esti-mate student support for building a food court on campus. To do this you wait outside the math building from 12pm to 3pm and ask every fifth student who leaves, ”Would you support building a new food court on campus?”. By the end of this time you ask 86 students. Out of these 61 report that they would support building a new food court on campus.
(a) What type of sampling was used here?
(b) Build a 99% confidence interval for the true proportion of students at your college who would support building a food court on campus. Make sure to check all necessary conditions and interpret your interval.
(c) Using your interval from part (a) could you argue that the majority of students support building a new food court on campus? Why or why not?
(d) What is the most likely form of bias your study suffered from?
Question 4) Suppose you want to measure the current proportion of El Camino students (recall there are approximately 20000 El Camino students) that use a car, bus or other automoblie to get to school. To do this you take a random sample of 65 El Camino students and ask them if they use a car, bus, or other automobile to get to school. 61 of the people respond that they do use a car, bus, or other automobile.
(a) Confirm 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 who use a car, bus, or other automobile to get to school. Make sure to interpret your interval.
Question 5) 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 α=.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 atα=.01 or α=.10
Question 6) You are interested in studying if men and women have different opinions on cheating in a relationship. To study this you take a random sample of 100 men and 200 women. You ask all of them, ”Would you continue to be in a relationship with a person who cheated on you, even though cheating is a horrible act that clearly destroys the trust between two people?”. 20 men respond that they would continue the relationship and 25 women respond that they would continue the relationship.
(a) Carry out a hypothesis test at α = .05 to test the claim that men and women have differ-ent opinions on cheating in a relationship. Make sure to confirm all necessary conditions. State your conclusion in context of the situation.
(b) If you were worried about falsely claiming there was difference between men and women, would you want to retest atα =.01 or α=.1? Why?
(c) What might be one source of bias in your study?
Question 7) Consider the following data showing results from a survey of 150 El Camino stu-dents about their major and their experiences in taking math classes at El Camino.
Enjoyed Neutral Did Not Enjoy
STEM 23 10 7
Social Sciences 25 16 19
Arts and Humanities 11 23 16
(a) Carry out a hypothesis test at α = .05 to test if there is a relationship between major and enjoyment of math classes. Make sure to confirm all necessary conditions.
(b) Describe what it would mean to make a Type I error here. (c) Describe what it would mean to make a Type II error here.
Question 8) Suppose that you want to study if for El Camino students success on a basic grammar test is related to success on a basic math test. (Recall their are approximately 20000 El Camino students) 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 83 30
Failed Grammar 12 25
(a) Carry out a hypothesis test at α =.05 to see if there was evidence that El Camino students’ success on these two tests were related. 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.
Question 9) 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 α = .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.
Question 10) Suppose you work for a town government (around 40000 adult residents). You are studying the ethnic diversity of your area. From previous research in 2012 you had the following ethnic breakdown:
Whte 25%, Hispanic 30%, African-Amerian 10%, Asian 20%, Other or Multiple 15%
You take a random sample of 300 of the people living in your area and get the following results: White: 66, Hispanic: 114, African-American: 39, Asian: 51, Other or Multiple: 30
(a) Test at α = .05 to see if the ethnic diversity in your area has changed since 2012. Make sure to check all necessary conditions and state your conclusion in the context of this situation. (b) If you were worried about missing a change in the ethnic diversity of your area would you retest atα=.01 or α=.10? Why?
Question 11) Suppose a math department at a large university is interested in seeing if there three large lecture calculus classes are performing differently (Note: Each large lecture has around 250 students enrolled). To do this they take a random sample of 9 students from each class and record their course averages midway through the term. They get the following data:
Morning Lecture: 51,62,63,70,71,73,82,84,90 Afternoon Lecture: 65,76,77,79,79,85,87,89,93 Evening Lecture: 50,68,71,73,74,78,85,88,96
(a) Carry out a hypothesis test at α = .05 to see if there is evidence that the three classes are performing differently. Make sure to confirm 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.
