Economics 302 Quiz #1



Economics 302 Quiz #1

Professor Meyer Fall 1999

Name: _______________________________

1. Explain the difference between bias and sampling error. How can you reduce bias and sampling error in your statistics? (6 points)

Quoting from your textbook: “Sampling errors occur because of a large number of uncontrollable factors which we can subsume under the term chance.” Sampling error occurs because we are choosing a sample from the entire population and results will differ from sample to sample. Misreading instruments is another example of sampling error.

Bias, on the other hand, is a systematic error in the sampling technique or in the questions asked of respondents. This type of error is controllable.

In order to reduce sampling error, larger samples should be taken. In order to reduce bias, the investigator should take a truly random sample and be sure that he is controlling for all important factors.

2. Students in Econ 302C are categorized by year and gender in the table below. (16 points)

| |Male |Female |

|Class of 2000 |1 |2 |

|Class of 2001 |11 |6 |

a. If a random student from the class is chosen, what is the probability that the student will be female?

P(female) = 8/20 = 0.40

b. If a random student from the class is chosen, what is the probability that the student will be from the class of 2001?

P(2001) = 17/20 = 0.85

c. Are being in the class of 2001 and being female mutually exclusive events? Explain.

No, they are not. Mutually exclusive events cannot occur together. To prove that being in the class of 2001 and being female are not mutually exclusive, use the formal definition, which states that two events, A and B, are mutually exclusive if P(A and B) = 0. P(female and 2001) = 0.3 ( 0, so the events are not mutually exclusive.

d. Are being in the class of 2001 and being female independent events? Explain.

No, they are not. Independence means that the probability of one event occurring does not depend on whether or not the other event occurred. Formally, two events, A and B, are independent if P(A|B) = P(A).

P(2001|female) = 0.75 ( P(2001) = 0.85, so being female and being a member of the class of 2001 are not independent in this sample.

3. A quality control engineer want to test whether tires coming off a production line meet the customer’s specifications. He chooses five tires and measures their diameters as 30.01, 30.02, 30.03, 30.03, and 30.02. (16 points)

a. Is this a sample or a population?

This is a sample.

b. Find the mean of the 5 observations.

Mean = 30.02

c. Find the standard deviation of the five observations.

Standard Deviation = 0.0083668

d. What is the median diameter?

Median = 30.02

4. Suppose I wanted to test whether there was a relationship between IQ tests and grades in college. (12 points)

a. What type of graph might I construct to see the relationship?

I would use a scatterplot.

b. If I chose to run a linear regression using ordinary least squares, which variable would be my dependent variable? Which variable would be my independent variable?

Grades would be my dependent variable, and IQ test scores would be my independent variable, since the hypothesis that I would be testing is that college grades depend on IQ test scores.

c. Write down a general equation for the line that I would estimate.

I allowed a pretty wide range of answers here, but the most correct answer is Y = b0 + b1 * X + e

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download