Math Stats Exam Help

Final Exam - Review Questions Part 2 M243, Sum ’19

Q1 In a recent survey, college students were asked whether they’d prefer to fight (1) one hundred duck-sized horses, or (2) one horse-sized duck. Much to the researchers’ surprise, of the 34 people in the sample, 33 would choose to fight the one hundred duck-sized horses. Construct a 95% confidence interval for the proportion of college students that would choose to fight the horses.

Q2 You wish to test the claim “UO Students score higher on the ACT than the national average.” Suppose that scores for all students on the ACT are approximately Normal with mean 21 and standard deviation 3.7. You take a SRS of 20 UO students and ask what they scored on the ACT. Their scores are listed below.

22 23 22 24 24 20 22 22 21 21 19 25 21 20 24 27 25 18 21 23

Do UO students score higher on the ACT than the national average?

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Final Exam - Review Questions Part 2 M243, Sum ’19

Q3 PTC is a substance that has a strong bitter taste for some people and is tasteless for others. The ability to taste PTC is inherited; for example 75% of Italians can taste PTC. You want to estimate the proportion of US adults who can taste PTC, and from previous studies there is good evidence to suspect that the proportion of US adults who can taste PTC is the same as Italians.

(a) How large a sample (n) must you collect so that the margin of error of a 95% large-sample confidence interval for the proportion of US adults who can taste PTC is at most 0.04?

(b) Suppose you took a sample of US adults of size n and computed p̂ = 0.72. Is there a difference between the proportion of US and Italian adults who can taste PTC? Use the value of n from (a). If you weren’t able to find n, use n = 500 instead.

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Final Exam - Review Questions Part 2 M243, Sum ’19

Q4 “Do you drink coffee?” Researchers asked this question of a sample of 385 students. Of the 149 men in the sample, 101 said “yes.” Among the 236 women, 117 said “yes”.

(a) Verify that the conditions for using a large-sample confidence interval are met.

(b) At the 1% level, is there a significant difference between the proportions of men and women who drink coffee?

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Final Exam - Review Questions Part 2 M243, Sum ’19

Q5 A medical researcher wishes to determine whether there is a difference in heart rates (in beats per minute) between smokers and nonsmokers. Their data is shown below.

Sample size Sample mean Sample standard deviation Smokers n1 = 26 x1 = 63 s1 = 6.01

Nonsmokers n2 = 18 x2 = 55 s2 = 3.16

Construct a 99% confidence interval for the difference in mean heart rate between smokers and nonsmokers.

Q6 Two fair dice are rolled. What is the probability that the number on the first die was at least 4, given that the sum of the two dice was 8?

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Final Exam - Review Questions Part 2 M243, Sum ’19

Q7 A local dog groomer wishes to update their business model. To start this process, they wish to answer the question “On average, how many times per year does a local dog owner take their dog to be groomed?” To answer this, they attempt to conduct a survey.

a) On their first attempt, they stand outside of the local dog park and ask this question to passersby. Name two types of bias that could occur with this sampling design.

b) Describe an improved sampling design that could eliminate both types of bias mentioned above.

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