14. In a chapter Preview we presented a study showing that handling money reduces the perceptionpain (Zhou, Vohs &Baumeister, 2009). In the experiment a group of college students was told that theywere participating in a manual dexterity study. Half of the students were given a stack of money tocount and the other half got a stack of blank paper. After the counting task, the participants were askedto dip their hands into bowls of very hot water (122° F) and rate how uncomfortable it was. Thefollowing data show ratings of pain similar to the results obtained in the study.|Counting MoneyCounting paper78111013108117151214510(a) Is there a significant difference in reported pain between the two conditions? Use a two-tailed testwith a = 0.01.(b) Compute Cohen's d to estimate the size of the treatment effect.wwww

Name: 14. In a chapter Preview we presented a study showing that handling m
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Description: 14. In a chapter Preview we presented a study showing that handling money reduces the perceptionpain (Zhou, Vohs &Baumeister, 2009). In the experiment a group of college students was told that theywere participating in a manual dexterity study. Half

In the experiment, a group of college students was told that they were participating in a manual dexterity study. Half of the students were given a stack of money to count and the other half got a stack of blank paper. After the counting task, the participants were asked to dip their hands into bowls of very hot water (122° F) and rate how uncomfortable it was. The following data show ratings of pain similar to the results obtained in the study. Counting Money Counting Paper 7 9 8 11 10 13 6 10 8 11 5 9 7 15 12 14 5 10 We need to test whether there is a significant difference in reported pain between the two conditions. Let µ1 = average ratings of participants in the first group and µ2 = average ratings of participants in the second group. Hence, we test whether the population means for these two groups are different. Let us assume that the samples are taken from the normally distributed populations.To test the claim about equality of means for two normally distributed populations, we use either the Z test or t test. If the population standard deviations are known then we use Z test otherwise we use t test. If population standard deviations are unknown then we either assume the equality of standard deviations (that is, σ1 = σ2) or assume that these are not equal (that is, σ1 and σ2 are not same). If we assume σ1=σ2 then we use pooled variance otherwise we use unpooled variance. Here in this example, two samples are equally dispersed. Therefore, we assume the population standard deviations are equal and use pooled standard deviation. The null and alternative hypotheses in this case can be stated as follows; H0 : µ1 = µ2 Vs H1 : µ1 ≠ µ2 Since the alternative hypothesis (H1) contains "≠" sign, the test is two tailed test. The degrees of freedom (df) for two sample t test with pooled variance are, n1+n2-2 = 9+9-2 =16. The critical value at significance level, α = 0.01 is given by, tc = 2.9208. This is calculated using excel formula, "=T.INV.2T(α,df)" The formula for test statistic and degrees of freedom in this case are as follow. While the Cohen’s d to estimate the size of the treatment effect is given by the formula, Here sp is pooled standard deviation given by the formula, The sample mean and sample standard deviation can be calculated using the formula, Using these formulas stated above we get, the sample means and sample standard deviations for the two samples as follows; The pooled standard deviation sp is, This gives the calculated value of test statistic as, Moreover, the Cohen’s d to estimate the size of the treatment effect is as follows,Let tc be a critical value and t0 be a calculated test statistic value. Then the decision rule for the two-tailed test based on critical value tc can be stated as, If t0 ≤ -tc or t0 ≥ tc then we reject hull hypothesis at α significance level otherwise we fail to reject null hypothesis. Since t0 = -3.5790 < -tc = -2.9208 we reject null hypothesis at 0.01 significance level. Conclusion: There is sufficient evidence to support the claim that there is significant difference between the average ratings of participants in the two groups. In other words, there is a significant difference in reported pain between the two conditions.