Chapter 1 Supplemental Homework

MATH136+ Chapter 1 Supplemental Homework Spring 2021
1. Hadey the goat is curious about how much data his neighborhood, Avocado Park, uses in a day. He divides the neighborhood into city blocks and randomly selects 4 of them for his research, which comes to 120 households. He cuts the cable lines to all of these households and installs data meters to measure the amount of data being sent into the household. Then, out of curiosity, he randomly selects half of the households and leaves notices on their doors that they will be charged extra for each TB they
download that month beyond a 9TB cap. Then he compares the daily downloads of all of the households.

a. Describe the population of interest in this study.
b. State all variables of interest in this study. For each variable, indicate whether it is qualitative, quantitative, discrete, continuous, binary, explanatory or response
(indicate all that apply) and state the level of measurement.
c. Is this an example of an observational study or a designed experiment? Justify your answer.
d. What method of sampling did Hadey employ?
e. What did Hadey assume in utilizing the sampling method you chose in part d?
f. Describe the elements of experimental design that Hadey is employing here. Be thorough.
g. Can you identify any potential sources of bias in Hadey’s research?
h. If the households that received notices stream significantly less data than the households that did not, can Hadey logically conclude that similar notices would cause reduction in streaming in the rest of Avocado Park? Justify your answer.
i. Bonus question: Hadey’s research has a glaring problem.  What is it?

2. Letecia the goatherd is always concerned about the mental wellbeing of her flock. She decides to take a quick poll, so she randomly chooses one of the first 23 goats at the feed trough one morning and asks them to rate their mental health on a scale from 1 to 10. She also asks them if the hay is satisfactory. She then asks every 23rd goat after that one to get her sample.
a. Describe the population of interest in this study.
b. State all variables of interest in this study. For each variable, indicate whether it is qualitative, quantitative, discrete, continuous, binary, explanatory or response
(indicate all that apply) and state the level of measurement.
c. Is this an example of an observational study or a designed experiment? Justify your answer.
d. What method of sampling did Letecia employ?
e. What did Letecia assume in utilizing the sampling method you chose in part d?
f. Describe the elements of experimental design that Letecia is employing here. Be thorough.
g. Can you identify any potential sources of bias in Letecia’s research?
h. If the goats expressing satisfaction with the hay tended to have mental health scores, can Letecia logically conclude that disappointing hay is harming her goats mental health? Justify your answer.
i. Bonus question: If Letecia does notice a significant difference in the mental health scores of the satisfied vs. the dissatisfied goats, what other explanation could there
be for this phenomenon than that not liking the hay is depressing the goats?