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Chapter 14: Problem 6

The article "Why We Fall for This" (AARP Magazine, May/June 2011 ) describes an experiment investigating the effect of money on emotions. In this experiment, students at University of Minnesota were randomly assigned to one of two groups. One group counted a stack of dollar bills. The other group counted a stack of blank pieces of paper. After counting, each student placed a finger in very hot water and then reported a discomfort level. It was reported that the mean discomfort level was significantly lower for the group that had counted money. In the context of this experiment, explain what it means to say that the money group mean was significantly lower than the blank- paper group mean.

Short Answer

Expert verified
When it is said that the money group mean was significantly lower than the blank-paper group mean, it means that the average discomfort level reported by the group of students who counted money was not only lower, but 'significantly' lower implying a high level of certainty in the influence of money counting to lessen discomfort. The term 'significantly' indicates statistical significance, meaning the likelihood of the result being a fluke of chance is very low.

Step by step solution

01

Understanding the Context

Firstly, the experiment context needs to be comprehended. Here the study is about the psychological effect of money on feelings of discomfort. Two groups were formed with one counting money and the other counting blank papers. After that, they were subjected to a discomforting situation, and they reported the discomfort level.
02

Understanding the Results

The reported discomfort level formed the sample data for the study. The mean discomfort level for the group that counted money was 'significantly lower' than the blank-paper group. The term 'significantly' is a statistical term implying that the result (lower mean discomfort in money group) is not just due to random chance but a real effect (the influence of money on discomfort level). This is generally checked using various statistical tests.
03

Interpreting the Meaning

Saying that the 'money group mean was significantly lower than the blank-paper group mean' refers to the fact that the numerical average of discomfort levels reported by the money group students was not merely lower, but 'significantly' lower, meaning there's a high degree of certainty that counting money had an actual effect on reducing discomfort. The term significantly often implies the results were statistically significant, stating that it's very unlikely these results happened by chance.

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Most popular questions from this chapter

The paper "Matching Faces to Photographs: Poor Performance in Eyewitness Memory" Uournal of Experimental Psychology: Applied [2008]: \(364-372)\) described an experiment to investigate whether people are more likely to recognize a face when they have seen an actor in person than when they have just seen a photograph of the actor. The paper states that there was no significant difference in the proportion of correct identifications for people who saw the actor in person and for those who only saw a photograph of the actor. In the context of this experiment, explain what it means to say that there is no significant difference in the group means.

In the paper "Happiness for Sale: Do Experiential Purchases Make Consumers Happier than Material Purchases?" (Journal of Consumer Research [2009]: \(188-197\) ), the authors distinguish between spending money on experiences (such as travel) and spending money on material possessions (such as a car). In an experiment to determine if the type of purchase affects how happy people are after the purchase has been made, 185 college students were randomly assigned to one of two groups. The students in the "experiential" group were asked to recall a time when they spent about \(\$ 300\) on an experience. They rated this purchase on three different happiness scales that were then combined into an overall measure of happiness. The students assigned to the "material" group recalled a time that they spent about \(\$ 300\) on an object and rated this purchase in the same manner. The mean happiness score was 5.75 for the experiential group and 5.27 for the material group. Standard deviations and sample sizes were not given in the paper, but for purposes of this exercise, suppose that they were as follows: \begin{tabular}{|ll|} \hline Experiential & Material \\ \hline\(n_{1}=92\) & \(n_{2}=93\) \\ \(s_{1}=1.2\) & \(s_{2}=1.5\) \\ \hline \end{tabular} Using the following Minitab output, carry out a hypothesis test to determine if these data support the authors' conclusion that, on average, "experiential purchases induced more reported happiness." Use \(\alpha=0.05\) Two-Sample T-Test and Cl Sample \(\begin{array}{rrrrr}\text { ple } & \text { N } & \text { Mean } & \text { StDev } & \text { SE Mean } \\ 1 & 92 & 5.75 & 1.20 & 0.13 \\ 2 & 93 & 5.27 & 1.50 & 0.16\end{array}\) Difference \(=\operatorname{mu}(1)-\operatorname{mu}(2)\) Estimate for difference: 0.480000 \(95 \%\) lower bound for difference: 0.149917 T-Test of difference \(=0(\mathrm{vs}>): \mathrm{T}\) -Value \(=2.40 \mathrm{P}\) -Value \(=\) \(0.009 \mathrm{DF}=175\)

14.32 Women diagnosed with breast cancer whose tumors have not spread may be faced with a decision between two surgical treatments-mastectomy (removal of the breast) or lumpectomy (only the tumor is removed). In a long-term study of the effectiveness of these two treatments, 701 women with breast cancer were randomly assigned to one of two treatment groups. One group received mastectomies, and the other group received lumpectomies and radiation. Both groups were followed for 20 years after surgery. It was reported that there was no statistically significant difference in the proportion surviving for 20 years for the two treatments (Associated Press, October 17,2002 ). Suppose that this conclusion was based on a \(90 \%\) confidence interval for the difference in treatment proportions. Which of the following three statements is correct? Explain why you chose this statement. Statement 1: Both endpoints of the confidence interval were negative. Statement 2: The confidence interval included \(0 .\) Statement 3 : Both endpoints of the confidence interval were positive.

Women diagnosed with breast cancer whose tumors have not spread may be faced with a decision between two surgical treatments -mastectomy (removal of the breast) or lumpectomy (only the tumor is removed). In a longterm study of the effectiveness of these two treatments, 701 women with breast cancer were randomly assigned to one of two treatment groups. One group received mastectomies and the other group received lumpectomies and radiation. Both groups were followed for 20 years after surgery. It was reported that there was no statistically significant difference in the proportion surviving for 20 years for the two treatments (Associated Press, October 17,2002 ). What hypotheses do you think the researchers tested in order to reach the given conclusion? Did the researchers reject or fail to reject the null hypothesis?

14.31 The online article "Death Metal in the Operating Room" (www.npr.org, December 24,2009 ) describes an experiment investigating the effect of playing music during surgery. One conclusion drawn from this experiment was that doctors listening to music that contained vocal elements took more time to complete surgery than doctors listening to music without vocal elements. Suppose that \(\mu_{1}\) denotes the mean time to complete a specific type of surgery for doctors listening to music with vocal elements and \(\mu_{2}\) denotes the mean time for doctors listening to music with no vocal elements. Further suppose that the stated conclusion was based on a \(95 \%\) confidence interval for \(\mu_{1}-\mu_{2},\) the difference in treatment means. Which of the following three statements is correct? Explain why you chose this statement. Statement 1: Both endpoints of the confidence interval were negative. Statement 2: The confidence interval included \(0 .\) Statement 3: Both endpoints of the confidence interval were positive.
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