Investigation 4: Anchoring phenomenon (assigned Tues Jan 19, due Fri Jan 22)

You may work with one other person on this assignment, handing in one report with both names. Word-processed reports are much preferred to hand-written ones. Please copy/paste relevant, well-labeled Minitab output into a Word file as appropriate.

Recall the data that we collected in class, when you were asked to guess the number of residents of Milwaukee, Wisconsin. Some of you were told that the nearby city of Chicago has a population of about 3 million people, while the rest of you were told that the nearby city of Green Bay, Wisconsin has a population of about 100 thousand. Previous studies have shown that these numbers serve as a psychological anchor, so people told about Chicago tend to guess a higher population for Milwaukee than people told about Green Bay. (I read about this in a book called Nudge: Improving Decisions About Health, Wealth, and Happiness.) My purpose in collecting the class data is to see if we find strong evidence of this anchoring phenomenon in our class.

a) Identify the explanatory and response variable in this study. Also classify each as categorical or quantitative.

b) Is this an observational study or an experiment? Explain.

c) Were the subjects in this study randomly selected from a population? Explain.

d) Were the subjects in this study randomly assigned to groups? Explain.

e) Express the null and alternative hypotheses (in symbols) for testing whether our class data gives strong evidence in support of the anchoring phenomenon described above.

The class data can be found in the Minitab worksheet Milwaukee252W10.mtw. Column 1 contains the guesses (in thousands, to the nearest thousand), and column 2 indicates which comparison city was presented to the student.

f) Produce (and submit) appropriate graphical displays and summary statistics for comparing guesses between the two groups. Comment on whether this descriptive analysis of the data suggests that the anchoring phenomenon is present in our class results.

g) Check and comment on whether the technical conditions for the validity of a two-sample t-test and t-interval are satisfied here.

h) Conduct a t-test of significance of the hypotheses that you stated in e). Report the test statistic and p-value. [Hint: You can do this by hand, or with Minitab by using Stat> Basic statistics> 2-Sample t …, Samples in one column] Also report your test decision at the a = .01 significance level. Finally, summarize your conclusion in context.

i) Produce a 95% confidence interval for the difference in population means between the two groups. [Hint: Again you can do this by hand or with Minitab. Minitab will only produce the confidence interval after you set the alternative to “not equal.”] Also write a sentence interpreting what this interval reveals.