A famous study of children at Stanford in 1972 involved researchers giving a child a marshmallow and then asking
the child to wait for 15 minutes with the promise of a second marshmallow if the child did not eat the rst. A
recent modication of this study looked at whether providing an unreliable or a reliable environment would aect
the length of time the child waited for a second marshmallow. Please consult the description of this study found
1. (5 points) In the Rochester study, what were the sample, the population, explanatory variable(s) and response
variables? (Hint: there are two responses variables: one a mean and one a proportion)
2. (20 points) The graphic on the page gives some indications of both sample mean and margin of error of the
provided condence intervals. While the description farther down the page identies the sample means of
the two groups exactly, nowhere is the sample standard deviation stated explicitly. Approximate the margin
of the error of the wait time in the unreliable environment" group and for the reliable environment" group,
then use those values to approximate the sample standard deviation of wait time for each group. (You should
have a total of two margins of error and two standard deviations when you are done)
3. (5 points) Nowhere in the news article is it stated how the sample of children was obtained, nor the underlying
distribution. In order to perform signicance tests for the mean wait time of children in each group, or for
the dierence in mean wait times between groups, what conditions need to be put on the sampling design
and distribution of values?
4. (30 points) There is clearly a signicant dierence in the mean wait time between the two groups. Construct
a 95% condence interval on the dierence in mean wait time between reliable and unreliable groups.
5. (5 points) Write a sentence explaining what the 95%" part of the condence interval from the previous
exercise means. The sentence should not refer to probability nor chance.
6. (30 points) Between the reliable and unreliable groups there is also clearly a dierence in the proportion
of children who waited the full fteen minutes. Construct a 95% condence interval for the dierence in
proportion of children in unreliable and reliable environments who waited for the full 15 minutes. (Make
sure that you pick a valid strategy, given what you know about the data)
7. (5 points) From the perspective of a researcher, how could you reduce the margin of error of the two-
proportion condence interval?
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Oct 14, 2020EXPERT
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