Determining Authorship and Household Composition - A Statistical Analysis

Scenario 1: Determining Authorship Based on Peculiar Patterns in Writing

An old document was found recently, but the author of this document is uncertain. Some believe the document was written by the famous author Reed A. Book, but they cannot determine this for certain. One statistical way we could determine this is by finding peculiar patterns in this author’s writing. Based on Book’s writing that we know he wrote, we know that the word “whereas” is used in 8% of his sentences. This newly found document consists of 140 sentences, and 4 of them have the word “whereas” in it. Does this data reflect the patterns of “whereas” usage of this author, or is this usage too low for the document to have been written by that author?

1.Describe the null hypothesis that we are testing in this scenario. 

2.Create a sampler in TinkerPlots that reflects this null hypothesis, and answer the following questions:

a.What did you set “draw” and “repeat” to? Explain.

b.What type of device did you select, and how did you choose the labels? Explain.

c.How does your device reflect the null hypothesis you described?

d.Paste an image of your sampler below:

3.Run one trial of your sampler model, and paste a plot of the results below. What does a single dot in that plot represent?

4.What measure will you collect statistics on and why? How will collecting statistics on this summary measure help you answer the research question?

5.Run 500 trials of the simulation and create a sampling distribution of the statistic of your choice. What does a single dot in this plot represent?

6.Find the p-value for this test, and re-paste an image of your sampling distribution that shows how you found the p-value.

7.Write up a conclusion in the context of the problem that answers the research question originally posed. Explain how your analysis determined this conclusion.

The 2010 US Census reported that 55.3% of households had no children. Today, there is a sense that younger couples are less likely to marry and/or have children. Thus, one might believe that this has led to this percentage increasing since 2010. Is this the case or has it remained roughly the same? A random sample of 500 US households was conducted in 2019, and they found that 288 of them had no children.

8.Describe the null hypothesis that we are testing in this scenario. 

9.Create a sampler in TinkerPlots that reflects this null hypothesis, and answer the following questions:

a.What did you set “draw” and “repeat” to? Explain.

b.What type of device did you select, and how did you choose the labels? Explain.

c.How does your device reflect the null hypothesis you described?

d.Paste an image of your sampler below:

10.Run one trial of your sampler model, and paste a plot of the results below. What does a single dot in that plot represent?

11.What measure will you collect statistics on and why? How will collecting statistics on this summary measure help you answer the research question?

12.Run 500 trials of the simulation and create a sampling distribution of the statistic of your choice. What does a single dot in this plot represent?

13.Find the p-value for this test, and re-paste an image of your sampling distribution that shows how you found the p-value.

14.Write up a conclusion in the context of the problem that answers the research question originally posed. Explain how your analysis determined this conclusion.