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Essentials of Statistics for the B...

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

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Section
BuyFindarrow_forward

Essentials of Statistics for the B...

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

Hallam, Price, and Katsarou (2002) investigated the influence of background noise on classroom performance for children aged 10 to 12. In one part of the study, calming music led to better performance on an arithmetic task compared to a no music condition. Suppose that a researcher selects one class of n = 18 students who listen to calming music each day while working on arithmetic problems. A second class of n = 18 serves as a control group with no music. Accuracy scores are measured for each child and the average for students in the music condition is M = 86.4 with SS = 1550 compared to an average of M = 78.8 with SS = 1204 for students in the no-music condition.

  1. a. Is there a significant difference between the two music conditions? Use a two-tailed test with α = .05.
  2. b. Compute the 90% confidence interval for the population mean difference.
  3. c. Write a sentence demonstrating how the results from the hypothesis test and the confidence interval would appear in a research report.

a.

To determine

To find: Whether there is a significant difference between the two music conditions using two tailed test with α=0.05.

Explanation

Given info:

Two sample each of size 18 have means 86.4 and 78.8 respectively. Their sum of squared difference (SS) equals 1,550 and 1,204 respectively.

Calculation:

Step 1: Null hypothesis is H0:μ1μ2=0 and alternate hypothesis is H1:μ1μ20

Step 2: For given t-statistics, degree of freedom equals:

df=n1+n22=18+182=34

For a two-tailed test with α=0.05 and df=34, the critical value (CV) is obtained from the t-table as t=±2.042

Step 3: obtaining t statistic.

Pooled variance:

sp2=SS1+SS2df1+df2=1,550+1,20417+17=275434=81

Thus, the pooled variance is 81

b.

To determine

To compute: The 90% confidence interval for the given question.

c.

To determine
The outcome of study the way it would be reported.

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