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Essentials of Statistics for the B...

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

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BuyFindarrow_forward

Essentials of Statistics for the B...

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

Research has shown that people are more likely to show dishonest and self-interested behaviors in darkness than in a well-lit environment (Zhong, Bohns, & Gina, 2010). In one experiment, participants were given a set of 20 puzzles and were paid $0.50 for each one solved in a 5-minute period. However, the participants reported their own performance and there was no obvious method for checking their honesty. Thus, the task provided a clear opportunity to cheat and receive undeserved money. One group of participants was tested in a room with dimmed lighting and a second group was tested in a well-lit room. The reported number of solved puzzles was recorded for each individual. The following data represent results similar to those obtained in the study.

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a. Is there a significant difference in reported performance between the two conditions? Use a two-tailed test with α = .01.

b. Compute Cohen's d to estimate the size of the treatment effect.

a.

To determine

To check: Whether there is significant difference in reported performance between the two conditions using two-tailed test with α=0.01

Explanation

Given info:

Two samples each of size 9 is given in the question. Two-tailed hypothesis test using α=0.01 is to be performed.

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=n1+n22=9+92=16

For a two-tailed test with α=0.01 and df=16, the critical value (CV)  is obtained from the t-table as t=±2.921

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

t=(M1M2)(μ1μ2)sM1M2

Software procedure:

Step-by-step procedure to obtain the sample mean and variance for the two groups, using the SPSS software:

  • Go to Variable View> Enter the name of the variable as Money and Paper.
  • Go to Data View>Enter the values ofMoney and Paper.
  • Choose Analyze > Descriptive Statistics> choose Descriptive.
  • Select Money and Paper and move it under variable(s)> Choose Options> Select Mean , Std. Deviation and Variance
  • ChooseContinue> choose OK.

Output using the SPSS software is given below:

From the SPSS output, the value of sample means, and variances are:

M1=7.56M2=11.33s12=5.27s22=4.75

Next, calculate pooled variance, sp2, using formula:

sp2=(df1)s12+(df2)s22df1+df2

Substitute 5.27 for s12, 4.75 for s22, 8 for both df1 and df2 in the above formula

sp2=(8)5

b.

To determine

To Find: The value of Cohen’s d for the given question.

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