   Chapter 10, Problem 16P 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

It appears that there is some truth to the old adage "That which doesn’t kill us makes us stronger" Seery, Holman, and Silver (2010) found that individuals with some history of adversity- report better mental health and higher Well-being compared to people with little or no history of adversity. In an attempt to examine this phenomenon, a researcher surveys a group of college students to determine the negative life events that they experienced in the past 5 years and their current feeling of well-being. For n = 18 participants with 2 or fewer negative experiences, the overage well-being score is M = 42 with SS = 398, and for n =16participants with 5 to 10 negative experiences the average score is M = 42 with SS = 370.a. Is there a significant difference between the two populations represented by these two samples? Use a two tailed lest with α = .01.b. Compute Cohen's d to measure the sire of the effect.c. Write a sentence demonstrating how the outcome of the hypothesis test and the measure of effect size would appear in a research report.

a.

To determine

To Find: If there is a significant difference between the two populations represented by the two samples using independent-measures t-test at α=0.01 for the given question.

Explanation

Given info:

Two samples with size 18 have mean 42 with SS as 398 and for n as 16 sample mean is 48.6 with SS as 370 respectively.

Calculations:

Step 1: Null Hypothesis is H0:μ1μ2=0 and Alternate Hypothesis is H1:μ1μ20

Step 2: For the given sample, the t-statistics will have degrees of freedom equals:

df=df1+df2=(n11)+(n21)=17+15=32

For an independent-measures test with α=0.01 and df=32, the critical value (CV) is obtained from the t-table as t=±2.7385.

Step 3: The t-statistics is calculated using formula:

t=(M1M2)(μ1μ2)sM1M2

The pooled variance, sp2, is calculated as:

sp2=SS1+SS2df1+df2=398+37017+15=76832=24

Now, the formula for estimated standard error of the difference is,

sM1M2=

b.

To determine

To Compute: The Cohen’s d to measure the size of the effect.

c.

To determine

To Describe: How does the outcome of hypothesis and measures of effect size appeared in research report.

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