# ECON 15B Study Guide - Midterm Guide: Drive Time, Sampling Distribution, Probability DistributionExam

by OC2657751

Department

EconomicsCourse Code

ECON 15BProfessor

Paul ShireyStudy Guide

MidtermThis

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TEST ONE

PROBABILITY AND STATISTICS, ECON 15B

JUNE 29, 2018

1. How are a sampling distribution of the mean and a sampling distribution of a proportion similar?

2 – 3. (Two questions – Twenty points) Let’s say that the average time it takes a UCI student to drive to campus is 42 minutes with a

standard deviation of 24 minutes. If we take a sample of 36 people, what is the probability that the average drive time for people in the

sample is 40 or more minutes? [Assume that the sampling distribution is approximately normal.]

4. There is a group of people. The average height of these people is 67 inches. Is it more likely to pick an individual who is more than

68 inches tall or a sample of four people who average more than 68 inches tall? Or are they probabilities equal? Or is it impossible to

tell? You do not have to explain your answer.

5. When does the sample have to be very large in order to ensure that the sampling distribution of the mean is approximately normal?

6 – 7. (Two questions – Twenty points) Let’s say that the favorite number of 36% of the people in Irvine is “three.” “Seven” is the

favorite number of 25% of the people; “ten” is the favorite number of 16% of the people; “thirteen” is the favorite number of 9% of the

people; and “one-hundred” is the favorite number of 14% of the people. If we take a sample of 16 people who live in Irvine, what is the

probability that 75% or more of the sample have “three” as their favorite number? [Assume it is safe to assume normality, and assume it

is safe to assume a continuous distribution.]

8. Why isn’t a voluntary sample considered to be a probability sample?

9. Is it ever the case that 𝐸(𝑋

̅)≠ 𝜇. Please explain.

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