Question

In: Statistics and Probability

Suppose we are interested in the effect of drinking on student achievement. We survey students at...

Suppose we are interested in the effect of drinking on student achievement. We survey students at the University of Rhode Island about their drinking habits - the number of times they “binge” drank (had 5+ drinks in one sitting) in the previous semester - and their previous semester’s GPA. We also have data on their gender, race, parent’s education, and family income. If we estimate the following regression:

GP Ai = β0 + β1BingeEventsi + γXi + i

Where GP Ai is student i’s GPA last semester, BingeEventsi is the number of times they reported binge drinking last semester, Xi is a set of controls for gender, race, and family variables, and i is the error term. Suppose we find a statistically significant negative correlation between binge drinking and GPA - increased binge drinking is associated with decreases in GPA (β1 < 0). Why does this finding not imply a causal effect of binge drinking on GPA?

Solutions

Expert Solution

In the question, it's written that Binge drinking is negatively correlated with GPA and it is statistically significant. Though, a big thing to note here is A correlation between two variables does not imply causation. This can be understood in a very simple way using this example:

There have been findings that there exists a negative correlation between a student's anxiety before an exam and the student's score on the test. But we cannot say that the anxiety causes a lower score on the test; there could be other reasons—the student may not have studied well, for example. So the correlation here does not imply causation.

Also, there exists a positive correlation between the number of hours one spends studying for a test and the grade he/she gets on the test. Here, there is causation as well; if you spend more time studying, it results in a higher grade.

So, this is why we can't infer there exists a causal effect of binge drinking on GPA in spite of being the fact that these two are negatively correlated.


Related Solutions

The minimum legal drinking age in the United States is 21. Suppose we conduct a survey...
The minimum legal drinking age in the United States is 21. Suppose we conduct a survey of students at URI. We collect data on their age (in months), the number of drinks they consumed in the last week, number of minutes of exercise in the last week, their body mass index (BMI), and other characteristics such as education, race, gender, class year, etc. Using this observational data, what would be an appropriate identification strategy if we are interested in estimating...
Suppose we are interested in knowing the effect of average number of cigarettes smoked by women...
Suppose we are interested in knowing the effect of average number of cigarettes smoked by women during pregnancy on infant birth weight ( in ounces). Suppose OLS regression estimates for the intercept and the slope coefficient are given as 119.77 and -.514 respectively. Interpret  and
A political science professor is interested in comparing the academic achievement characteristics of students who vote...
A political science professor is interested in comparing the academic achievement characteristics of students who vote in national elections and those of those who do not vote. In a random sample of 114 students who claim to have voted in the last presidential election, you see a mean of the mean scores of 2.5 and a standard deviation of 0.51. In an independent random sample of 123 students who have not voted, the mean of the mean scores is 2.97...
A student is interested in the sleep quality of students. That student selects a random sample...
A student is interested in the sleep quality of students. That student selects a random sample of 21 students (age 19-24 years) from each four undergraduate years (Freshman, Sophomore, Junior and Senior), and applies Pittsburgh Sleep Quality Index (PSQI) and obtains their responses. PSQI includes 19 self-reported items and is designed to evaluate overall sleep quality (Data are presented in Table 1 below). The student is interested in determining whether there is any evidence of a difference in sleep quality...
A graduate student in the School of Education is interested in whether families of students in...
A graduate student in the School of Education is interested in whether families of students in the Chicago Public Schools are for or against the new legislation proposing school uniform requirements. She surveys 600 students and finds that 480 are against the new legislation. Compute a 90 and 98 percent confidence interval for the true proportion who are for the new legislation.
You are interested in studying the effect of laptops in class on students’ performance. At the...
You are interested in studying the effect of laptops in class on students’ performance. At the beginning of the quarter, you randomly assign your 250 students to sit on either the left half or the right half of the lecture hall. Students on the left half are told to bring laptops to class and to take notes on their laptops. Students who sit on the right side of the room are required to write notes on paper. At the end...
20. A student is interested in studying the impact of the number of books students referred...
20. A student is interested in studying the impact of the number of books students referred to in a statistics course and the number of lectures they attended on the final grade on the course. A sample of 25 students is selected and the data are given below. BOOKS ATTEND GRADE 2 17 60 3 18 54 1 17 62 5 20 59 2 12 44 1 13 40 3 17 96 4 19 90 5 22 97 2 22...
Suppose we are interested in bidding on a piece of land and we know one other bidder is interested.
Suppose we are interested in bidding on a piece of land and we know one other bidder is interested. The seller announced that the highest bid in excess of $9,500 will be accepted. Assume that the competitor's bid x is a random variable that is uniformly distributed between $9,500 and $15,500.a. Suppose you bid $12,000. What is the probability that your bid will be accepted (to 2 decimals)?b. Suppose you bid $14,000. What is the probability that your bid will...
A student survey was completed by 446 students in introductory statistics courses at a large university...
A student survey was completed by 446 students in introductory statistics courses at a large university in the fall of 2003. Students were asked to pick their favorite color from black, blue, green, orange, pink, purple, red, yellow. (a) If colors were equally popular, what proportion of students would choose each color? (Round your answer to three decimal places.) (b) We might well suspect that the color yellow will be less popular than others. Using software to access the survey...
Suppose you are interested in the basic question of, “Is there an effect of mental health...
Suppose you are interested in the basic question of, “Is there an effect of mental health on amount of sleep?” You recruit 8 healthy individuals, 8 depressed individuals, and 8 anxious individuals and measure the amount they sleep. Given that   SSb = 1902 and    SSw = 3386 fill in a source table and find the obtained value of the appropriate statistic. a.17 b 5.90 c. 24.00 d. 4.45 Given your obtained value in the sleep study, what is the correct...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT