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STAT240 Homework 10 Solution
Preliminaries
This file should be in STAT240/homework/hw10 on your local computer.
Download superbowl_commercials.csv to STAT240/data .
Disclaimer
Many of these problems ask you to consider some true proportion. We have data on every commercial these brands have aired in Super Bowls in this time period, so the notion of a ‘population’ or ‘true parameter’ here is about a theoretical set of all advertisements that could have been created for Super Bowls, or if you prefer, about the probabilistic decision-making process that companies have to make behind the scenes (like the chimpanzee prosocial choices).
Statistical inference often requires us to consider unintuitive, theoretical populations like this. Understanding of this point is not required for doing the computations we request below, but is important to always keep in mind when conducting inference.
Problem 1
Each advertisement is classified according to several characterisitcs. More information can be found here.
Transform the data as follows:
Problem 2
Count the total number of ads in the dataset, as well as the total number of “Funny” ads. Build and interpret a 99% CI for (p_{funny}), the overall proportion of funny ads across all of the brands. Use the Agresti-Coull adjustment.
Problem 3
Repeat the analysis in problem 2, but build a 99% CI fo for (p_{funny}) with the Wald adjustment. How do the two intervals compare?
Problem 4
Perform a hypothesis test to determine whether more than half of superbowl ads are funny. Use hypotheses [H_0: p_{funny} = 0.5 quad ext{versus}quad H_A: p_{funny} > 0.5] and (alpha = 0.01). Interpret your result in context.
Please PRINT OUT YOUR p-value.
Replace this text with your response.
Problem 5
Replace this text with your response. (Model and assumptions)
Replace this text with your response. (Criticism)
Problem 6
Now, focus on (p_{H, funny}), which is the proportion of Hyundai ads that are funny. Perform a two-sided hypothesis test to determine whether or not half of all Hyundai ads are funny.
Please EXPLICITLY STATE your hypotheses, test statistic, null distribution, p-value, and conclusion.
Problem 7
Consider comparing the proportion of Hyundai ads that are funny to the proportion of Budweiser ads that are funny. Build a 95% confidence interval on the difference in proportions and use the Agresti-Coffe adjustment. Interpret your results in context.
Problem 8
Perform a hypothesis test to determine whether a different proportion of Hyndai ads than Budweiser ads are funny. Write appropriate twosided hypotheses and draw a conclusion with (alpha = 0.05).
Please EXPLICITLY STATE your hypotheses, p-value, and conclusion. No need to state the test statistic or null distribution.
This file should be in STAT240/homework/hw10 on your local computer.
Download superbowl_commercials.csv to STAT240/data .
Disclaimer
Many of these problems ask you to consider some true proportion. We have data on every commercial these brands have aired in Super Bowls in this time period, so the notion of a ‘population’ or ‘true parameter’ here is about a theoretical set of all advertisements that could have been created for Super Bowls, or if you prefer, about the probabilistic decision-making process that companies have to make behind the scenes (like the chimpanzee prosocial choices).
Statistical inference often requires us to consider unintuitive, theoretical populations like this. Understanding of this point is not required for doing the computations we request below, but is important to always keep in mind when conducting inference.
Problem 1
Each advertisement is classified according to several characterisitcs. More information can be found here.
Transform the data as follows:
Problem 2
Count the total number of ads in the dataset, as well as the total number of “Funny” ads. Build and interpret a 99% CI for (p_{funny}), the overall proportion of funny ads across all of the brands. Use the Agresti-Coull adjustment.
Problem 3
Repeat the analysis in problem 2, but build a 99% CI fo for (p_{funny}) with the Wald adjustment. How do the two intervals compare?
Problem 4
Perform a hypothesis test to determine whether more than half of superbowl ads are funny. Use hypotheses [H_0: p_{funny} = 0.5 quad ext{versus}quad H_A: p_{funny} > 0.5] and (alpha = 0.01). Interpret your result in context.
Please PRINT OUT YOUR p-value.
Replace this text with your response.
Problem 5
Replace this text with your response. (Model and assumptions)
Replace this text with your response. (Criticism)
Problem 6
Now, focus on (p_{H, funny}), which is the proportion of Hyundai ads that are funny. Perform a two-sided hypothesis test to determine whether or not half of all Hyundai ads are funny.
Please EXPLICITLY STATE your hypotheses, test statistic, null distribution, p-value, and conclusion.
Problem 7
Consider comparing the proportion of Hyundai ads that are funny to the proportion of Budweiser ads that are funny. Build a 95% confidence interval on the difference in proportions and use the Agresti-Coffe adjustment. Interpret your results in context.
Problem 8
Perform a hypothesis test to determine whether a different proportion of Hyndai ads than Budweiser ads are funny. Write appropriate twosided hypotheses and draw a conclusion with (alpha = 0.05).
Please EXPLICITLY STATE your hypotheses, p-value, and conclusion. No need to state the test statistic or null distribution.
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