   Chapter 15, Problem 15P Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570

Solutions

Chapter
Section Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570
Textbook Problem

a.

To determine

To Find: If the proportion of participants who claim to remember broken glass differ significantly from group to group for the given question.

Explanation

Given info:

A sample of 150 students were involved in a study based on “the response they gave regarding the broken glass or verb used for speed”. The distribution is given in the question. Use α=0.05 to test the claim.

 Yes No Total Smashed into 16 34 50 Hit 7 43 50 Control (not asked) 6 44 50 Total 29 121 150

Calculation:

Step 1: Null Hypothesis and Alternate Hypothesis are:

H0: Proportion of participants who claim to remember broken glass does not differ significantly from group to group.

H1: Proportion of participants who claim to remember broken glass differ significantly from group to group

Step 2: For the given sample, degrees of freedom equals:

df=(R1)(C1)   where R equals number of rows and C equals columns=(31)(21)=2

With α=0.05 and df=2, the critical value (CV)  is obtained from the χ2table as

χ2=5.991

Step 3: χ2statistic is calculated as:

χ2=(fofe)2fe

The formula to calculate expected frequency is:

fe=fcfrn...where fr is row frequency and fc is column frequency

Substitute n=600 in the above formula and compute respective values of expected frequencies:

For the category “smashed into”, the expected frequencies are:

fe,yes=29×50150fe,no=121×50150

For the category “Hit”, the expected frequencies are:

fe,yes=29

b.

To determine

To Find: The value of Cramer’s V for the given question.

c.

To determine

To Describe: How does the phrasing of the question influenced the participants memories.

d.

To determine

How would the outcome of hypothesis and Cramer’s V will be written in the report.

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