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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

In a recent study, Piff, Kraus, Côté, Cheng, and Keltner (2010) found that people from lower socio- economic classes tend to display greater prosocial behavior than their higher-class counterparts. In one- part of the study, participants played a game with an anonymous partner. Part of the game involved sharing points with the partner. The lower economic class participants were significantly more generous with their points compared with the upper-class individuals. Results similar to those found in the study, show that n = 12 lower-class participants shared an average of M =5.2 points with SS =11.91, compared to an average of M = 4.3 with SS = 9.21 for the n = 12 upper-class participants.

  1. a. Are the data sufficient to conclude that there is a significant mean difference between the two economic populations? Use a two-tailed test with α = .05.
  2. b. Construct an 80% confidence interval to estimate the size of the population mean difference.

a.

To determine

To Find: If there is a significant mean difference between the two economic populations using two-tailed test at α=0.05 for the given question.

Explanation

Given info:

Two samples each with size 12 have means 5.2 and 4.3 respectively. Similarly, both of them have sum of squared difference (SS) equal to 11.91 and 9.21 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=n1+n22=12+122=22

For a two-tailed test with α=0.05 and df=22, the critical value (CV)  is obtained from the t-table as t=±2.074

Step 3: t-statistics is calculated using formula:

t=(M1M2)(μ1μ2)sM1M2

But before that calculate pooled variance,sp2, using formula:

sp2=SS1+SS2df1+df2

Substitute 11.91 for SS1, 9.21 for SS2, 11 for both df1 and df2 in the above formula

sp2=11.91+9.2111+11=21.1222=0.96

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

sM1M2=sp2n1+sp2n2

Substitute 0

b.

To determine

To Find: The 80% confidence interval to estimate the size of the population mean difference  for the given question.

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