Stats Solutions

[Solved] Consider the following hypothetical. A professor obtains funding to sample tort cases that were filed in the lowest level courts of general jurisdiction

Question: Consider the following hypothetical. A professor obtains funding to sample tort cases that were filed in the lowest level courts of general jurisdiction in a particular state in 2010. After the cases are sampled, the professor's research team codes a number of attributes of each case, including the nature of the dispute and the legal issues involved in the case, the identities of the litigants, and the resolution of the case. The number of tort cases before these courts during this year was approximately 60,000. The professor's team uses simple random sampling to select 1,700 cases from this population. Five research assistants code each case and the inter-coder agreement on all coded items is extremely high. The data are eventually made public.

As an initial analysis, you want to make descriptive inferences about whether summary judgement occurs more often in cases with individual defendants or business defendants in the full population of cases. We are interested in $\pi_{i n d}$, the population proportion of summary judgements for individual defendants, and $\pi_{b u s}$, the population proportion of summary judgements for business defendants,.

In our random sample, 1000 cases have an individual defendant $\left(n_{i n d}=1000\right)$ and 21 of these resulted in summary judgment. Of the 700 cases with a business defendant, 29 resulted in summary judgement.

(5 points)

Form a large sample $95 \%$ confidence interval for $\pi_{i n d}$.
Provide an interpretation of this confidence interval in terms of the cases with individual defendants.
Form a large sample $95 \%$ confidence interval for $\pi_{b u s} .$
Do the $95 \%$ intervals for $\pi_{i n d}$ and $\pi_{b u s}$ overlap? What does this imply about whether the $99 \%$ intervals overlap?
Explain whether using $t$ -quantiles instead of the large sample $Z$ -quantiles would be justifiable from a theoretical perspective. Explain, whether it would matter from a practical perspective.

b) (2 points)