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Statistics

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Jun 6, 2024

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STAT 312 Spring 2024 Investigation 7: Mandela age guesses (assigned on Wed May 29, due on Thur June 6) You may work with in a group of as many as three students on this assignment, provided that you all contribute to the work. Type your answers to these questions into a file. (You do not need to re-type the questions.) Then save that file as a pdf file, and submit the pdf file in Canvas. Only one member of the group should submit a pdf file, making sure that all group member names appear at the top of the document. Recall that we gathered data in class near the beginning of this term, about your guesses for Nelson Mandela’s age when he died. We did this to investigate the psychological phenomenon known as anchoring. Two versions of the question were distributed to students: Version A: Nelson Mandela was the first black president of South Africa following apartheid. Was Mandela younger or older than 12 years old when he died? ____________ Make a guess for Mandela’s age (in years) when he died. ________ Version B: Nelson Mandela was the first black president of South Africa following apartheid. Was Mandela younger or older than 120 years old when he died? ____________ Make a guess for Mandela’s age (in years) when he died. ________ a) Identify the observational units, explanatory variable, and response variable. Also classify each variable as categorical or numerical. - Observational units: students in the 6-8PM STAT 312 class with Prof Rossman - Explanatory variable: the first question asking if he was younger/older than a certain age o categorical - Response variable: age of Nelson Mandel when he died o numerical b) Is this an observational study or a randomized experiment? Did we make use of random sampling, random assignment, both or neither? - Randomized experiment. - No, it did not include random sampling because the students in the class do not represent the population. - Yes, it did include random assignment because the papers with the different questions were shuffled before given out to the students in the class. Data from our class appear in the file MandelaAgeGuessesS24.txt , which is available in Canvas. You will use an applet called Descriptive Statistics , also available from a link in Canvas, to analyze these data. After you open the applet:

1. Click on the “Clear” button below the box containing the (default) dataset. 2. Copy/paste the Mandela age guess data from the file into the empty data box. 3. Click on the “Use Data” button. 4. Make sure that 65 appears as the sample size. 5. Select the quantitative (numerical) variable to be “age_guess”. 6. Select “anchor_value” for the “Separate by” variable. 7. Click on “Add Boxplot” below the graphs. c) Include a screen capture of the dotplots and boxplots in your file/report. d) Report the values of the sample size, mean, and standard deviation for each group. (Use the applet to calculate these by clicking on “Actual” beside “Mean” and “Std dev”.) - B120 o Sample size: 31 o Mean: 84.516 o Standard Deviation: 16.221 - A12 o Sample size: 34 o Mean: 65.588 o Standard Deviation: 16.666 e) Conduct a two-sample t-test for investigating whether students who saw the larger (120) anchor value tend to make larger age guesses, on average, compared to students who saw the smaller (12) anchor value. (Use the Theory-Based Inference applet, which is

available in Canvas, for the calculations. Select the “Two means” scenario, enter the values of the statistics, click on “Test of significance,” and select the appropriate alternative hypothesis.) Report the null and alternative hypotheses (in symbols), and the values of the test statistic and pvalue. - H o : μ 1 - μ 2 = 12 - H a : μ 1 - μ 2 >12 - t = 1.70 - p-value= 0.0473 - df = 62.72 f) Summarize your conclusion from the hypothesis test about the anchoring phenomenon. - Since our p value of 0.0473 is less than our significance level of 0.05, we reject the null. There is strong evidence that the difference of population means of Nelson Mandela age guesses between group one and group two is greater than 12. g) Determine a 95% confidence interval for the difference in population means between the two groups. (Again use the Theory-Based Inference applet for the calculations.) Report the endpoints of the interval. - (10.7715, 27.0845) h) Summarize what the confidence interval reveals about the anchoring phenomenon. - We are 95% confident that the difference of population mean of correct Nelson Mandela age guesses is between 10.7715 and 27.0845. i) Is it appropriate to draw a cause-and-effect conclusion from these data? If so, between what cause and what effect? Justify your answer. - It is appropriate to draw a cause-and-effect relationship conclusion from this data because the experiment included random assignment. The wording of the first question caused people to answer with higher or lower numbers for the second question. The cause was the first question’s wording and the effect was the answer to the second question. © 2024 Allan J. Rossman STAT 312 – Spring 2024 2

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