Download STAT 200 QUIZ 2 Solutions

STAT 200 QUIZ 2 Solutions
Questions 1 to 4 (40pts) correspond to the following statement:
A study collected data for 19 developed nations on yearly wine consumption and yearly
deaths from heart disease. The least-squares regression line for predicting heart
disease death rate from wine consumption is y-hat = 260.56 – 22.97 x.
1. Fill in the blank. The yearly wine consumption is the explanatory variable.
2. Fill in the blank. The heart disease death rate is the response variable.
3. The correlation for these variables is r = -0.843. About what percent of the
variation among countries in heart disease death rates is explained by the straight-line
relationship with wine consumption? Answer:
𝑟 2 = −0.8432 = 0.710649 ≈ 71%
4. Use the equation to predict the heart disease death rate in another country where
adults average 4 liters of alcohol from wine each year.
𝑦 = 260.56 − 22.97 × 4 = 168.68
Questions 5 to 6 (20pts) correspond to the following statement:
A political scientist wants to know how college students feel about the Social Security
system. She obtains a list of the 3456 undergraduates at her college and mails a
questionnaire to 250 students selected at random. Only 104 questionnaires are
returned.
5. What is the population in this study? College students
6. What is the sample from which information was actually obtained?
104 students who returned questionnaires
Questions 7 to 8 (20pts) correspond to the following statement:
An automobile manufacturer claims the mean gasoline mileage of all vehicles of a certain
type is 24 MPG. A random sample of mileages from 12 of the vehicles has a mean of 23.45
MPG. Is each of the bold numbers a parameter or a statistic? Answer below.
7. The mean mileage of 24 MPG is a parameter.
8. The mean mileage of 23.45 MPG is a statistic.
Questions 9 to 10 (20pts) correspond to the following statement:
Musical styles other than rock and pop are becoming more popular. A survey of college
students finds that 40% like country music, 30% like gospel music, and 60% like either
country or gospel music.
Event A: a student likes country music, 𝑃 𝐴 = 0.4
Event B: a student likes gospel music, 𝑃(𝐵) = 0.3
Event A or B : a student likes either gospel or country, 𝑃(𝐴 ∪ 𝐵) = 0.6
9. What is the probability that a randomly selected college student doesn’t like gospel or
country music? (Hint: This is the complement of the event that a student likes either
gospel or country music)
P(A ∪ B)c = 1 − P A ∪ B = 1 − 0.6 = 0.4
10. What is the probability that a randomly selected college student does not like country
music?
𝑃 𝐴𝑐 = 1 − 0.4 = 0.6