two pictures please answer all parts. fill in square boxes and the rest... Score

Question

two pictures please answer all parts. fill in square boxes and the rest...

Score: 13 A Aa 18. Chapter 10, Problem 14 of In a study showing that handling money reduces the perception pain (Zhou, Vohs, & Baumeister, 2009), a group were participating in a manual dexterity study. Half of the students were given a of money to count and the other half got a stack of blank pieces of paper. After the counting task, the were asked to dip their hands into bowls of very hot water (122°F) and rate how uncomfortable it was. The following data represent results similar to those obtained in the study Counting Money Counting Paper 9 10 6 8 13 10 9 15 14 10 12 Is there a significant difference in reported pain between the two condit ons? Use a two-tailed test with or·-01. (Use three decimal places for the standard error and the critical values, two for the other entries.)

Explanation / Answer

Solution:

Here, we have to use two sample t test for the population means assuming equal population variances. The null and alternative hypotheses for this test are given as below:

H0: µ1 = µ2 Versus Ha: µ1 µ2

This is a two tailed test.

We are given a level of significance or alpha value as 0.01.

= 0.01

We are given

Population 1 Sample

Sample Size

9

Sample Mean

7.555556

Sample Standard Deviation

2.297341

Population 2 Sample

Sample Size

9

Sample Mean

11.33333

Sample Standard Deviation

2.179449

Population 1 Sample Degrees of Freedom

8

Population 2 Sample Degrees of Freedom

8

Total Degrees of Freedom

16

Pooled variance = Sp2 = [((N1 – 1)S1^2 + (N2 – 1)S2^2)/(N1 + N2 – 2)]

Pooled variance = Sp2 =[(8*2.297341^2 + 8*2.179449^2)/16]

Pooled variance = Sp2 = 5.0139

Standard error = sqrt[Sp2 ((1/N1)+(1/N2))]

Standard error = sqrt[5.0139*((1/9)+(1/9))]

Standard error = 1.0556

Test statistic formula is given as below:

t = (X1bar – X2bar) / sqrt[Sp2 ((1/N1)+(1/N2))]

Where, Sp2 = [((N1 – 1)S1^2 + (N2 – 1)S2^2)/(N1 + N2 – 2)]

(X1bar – X2bar) = 7.555556 - 11.33333 = -3.7778

t = -3.7778 / 1.0556

t = -3.5789

Critical value = 2.9208 (by using t-table)

P-value = 0.0025 (by using t-table)

P-value < = 0.01

So, we reject the null hypothesis

Conclusion:

Reject the null hypothesis; there is a significant difference in the amount of pain experienced after counting money versus counting paper.

Population 1 Sample

Sample Size

9

Sample Mean

7.555556

Sample Standard Deviation

2.297341

Population 2 Sample

Sample Size

9

Sample Mean

11.33333

Sample Standard Deviation

2.179449

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