MATH
invest_3ed.pdf

# X enter the two columns in the graph variables box

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x Enter the two columns in the Graph variables box. Press OK . (i) Also calculate descriptive statistics (mean and standard deviation) of the melting times as before (using the stacked data in R, putting both columns in the Variables box in Minitab). Chocolate mean: Peanut butter mean: Chocolate SD: Peanut butter SD: How do the distributions of melting times, as revealed by these graphs and descriptive statistics, compare to your earlier analysis (from the randomized comparative experiment)? (j) Would it be valid to carry out a two-sample t -test to compare the average chocolate chip times to the average peanut butter chip times for these new data (matched pairs experiment)? Explain. When the data are paired (e.g., repeat observations on the same individual) we should not treat them as independent samples as you considered doing in (i) and (j). This ignores the information that two measurements were taken for each person (we couldn’t mix up the values in the s econd column without altering the information in the data). Instead you can analyze the differences in the times per person.

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Chance/Rossman, 2015 ISCAM III Investigation 4.8 291 (k) Calculate the differences between the chocolate chip times and the peanut butter chip times for each person (chocolate pean ut butter). [In R, you may have to attach “chiptimes” again.] Examine and describe a dotplot and descriptive statistics for these differences. Do they support a tendency for one chip to melt more slowly than the other? How are you deciding? Mean difference: Standard deviation of differences: (l) Does the pairing in the study design appear to have been helpful here? To decide, compare the standard deviation of the differences to the individual peanut butter and chocolate chip standard deviations. (m) Do you believe the evidence for a difference between chocolate chips and peanut butter chips is stronger, weaker, or similar to the strength of evidence from the completely randomized design? In particular, do you think a p-value we might get from these differences will be larger, smaller, or similar to what you would find from a two-sample t -test? Explain, being sure to consider factors that affect the size of a p-value when comparing a quantitative response variable between two groups. (n) Consider the following results from a paired experiment. Suggest a scenario where the paired data would be pretty convincing that the chocolate chip melting time is shorter, despite the substantial overlap between the two distributions. Then suggest a scenario where the data are paired but a significant difference is not found in the melting times.
Chance/Rossman, 2015 ISCAM III Investigation 4.8 292 Discussion: Typically when we collect data on chip melting data from our students, it is difficult to find a statistically significant difference between the melting times of the two types of chips because there is so much person-to-person variability in the melting times (and therefore a lot of overlap in the two distributions). One way to control for this person-to-person variability is to have each person melt both

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