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https://docs.google.com/spreadsheets/d/11bxYVh9whx_Po-bJhp-yN5-K1X8jNqRfKQD3sNH7

ID: 3312116 • Letter: H

Question

https://docs.google.com/spreadsheets/d/11bxYVh9whx_Po-bJhp-yN5-K1X8jNqRfKQD3sNH73Do/edit?usp=sharing

Among our sample of police incidents, 20 occurred in 2015 in the Tenderloin district. Of these, 8 incidents went unresolved (Resolution = “None”):

1) Use either binom test or pbinom to compute a p-value for testing H0 : p = 0.25 vs. Ha : p > 0.25. What is the p-value? Answer to four significant figures.

2) Consider the times at which the above 20 incidents occurred, by resolution status:

Use the bootstrap with B = 500 to construct a 95% confidence interval for sd of time res

sd of time unres
So that our answers match, first run set.seed(101) to initialize R’s random number

generator.

What is the confidence interval?

i. [0.25,2.08]

ii. [0.91,1.02]

iii. [0.70,1.18]

iv. [0.39,2.37]

b)   To test H0 : res = unres vs. Ha : res = unres, carry out a two-sample t-test assuming equal variances; you can use the t.test function with argument var.equal = TRUE. What is the p-value? Answer to four significant figure

c) Make QQ plots for time res and time unres. Based on the plots, which of the following is most reasonable?

i. Both variables are normally distributed.
ii. The time res variable is normally distributed, but time unres is not.

iii. The time unres variable is normally distributed, but time res is not.

iv. Neither variables are normally distributed.

Explanation / Answer

Solving Q1.

Using binom test:

> binom.test(x = 8, n = 20, p = 0.25, alternative = "greater", conf.level = 0.95)

Exact binomial test

data: 8 and 20

number of successes = 8, number of trials = 20, p-value = 0.1018

alternative hypothesis: true probability of success is greater than 0.25

95 percent confidence interval:

0.2170686 1.0000000

sample estimates:

probability of success

0.4

The p-value = 0.1018