# ECON 15B Study Guide - Midterm Guide: Null Hypothesis, Test Statistic, Standard DeviationExam

by OC2657751

Department

EconomicsCourse Code

ECON 15BProfessor

Paul ShireyStudy Guide

MidtermThis

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TEST FOUR

PROBABILITY AND STATISTICS, ECON 15B

JULY 20, 2018

1 – 2. (Two questions – Twenty points) There is a sample of 25 boys and a sample of 40 girls. Ten of the boys have read Novel X,

and ten of the girls have read Novel X. Use a χ2 test to see if gender and reading Novel X are independent. You need to calculate the test-

statistic, state the critical value, come to a conclusion about the null hypothesis, and state what this means concerning the association

between gender and Novel X. Let α = .05.

3. What’s the major difference between when you use a χ2 test for independence and a χ2 test goodness-of-fit test?

4. We have taken a sample of a bag of Skittles Rainbow Candy. It is supposed to be 30% red, 20% yellow, 20% green, 20% orange,

and 10% purple. What is the smallest sample we can have and still have a chi-square test valid?

5 – 6 (Two questions – Twenty Points). Let’s suppose we had a sample of 200 Skittles. (We are continuing with the situation in

question 4.) We got 70 red, 30 yellow, 44 green, 36 orange, and 20 purple Skittles. Please calculate the chi-square statistic, state the

critical value, state what we conclude concerning the null hypothesis; and come to a conclusion concerning Skittles.

7 – 8. Ian is comparing people who live in Northern California and Southern California. He wants to know if they have different

beliefs concerning “The Big Idea.” His null hypothesis is the proportion of people in Northern who believe the Big Idea is true is equal to

the proportion of people in Southern California who believe the Big Idea is true. Thus, his null hypothesis is PN = PS where N is

Northern California and S is Southern California. He collects a sample of 50 people from Northern California, 30 of whom believe the

Big Idea is true. He collects a sample of 40 people from Southern California, 16 of whom believe the Big Idea is true. Calculate the z-

statistic, state the critical value, come to a conclusion about the null hypothesis, and state what this means concerning the difference

between the north and the south.

9. (Continuing with the above question) Barbara, who lives in Burney in the far northern part of California, doesn’t consider San

Francisco and Sacramento to be in Northern California. They are in the central part of the state. Thus, she wants to replicate Ian’s study,

but make the null hypothesis PS = PN = PC, where C stands for the central part of California. Is it possible to do this experiment? If so,

how would we do it; if not, explain why not.

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