Incumbent local exchange carriers such as Verizon, install and maintain local land-based telephone lines, lease capacity

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

## CLEC

Incumbent local exchange carriers (ILECs), such as Verizon, install and maintain local land-based telephone lines, lease capacity, and perform repairs for the competing local exchange carriers (CLECs). The law requires that ILECs perform repairs in the same timely manner as that provided to their own customers. The repair times (in hours) of 95 service requests from customers of Verizon and 10 requests from customers of a CLEC during the same time period were collected. The following code contains the collected data along with code to perform an F-test on the data.

```r

# Data

ilec <- c(1,1,1,1,2,2,1,1,1,1,2,2,1,1,1,1,2,2,1,1,1,1,2,3,1,1,1,1,2,3,1,1,1,1,2,3,1,1,1,1,2,3,1,1,1,1,2,3,1,1,1,1,2,3,1,1,1,1,2,4,1,1,1,1,2,5,1,1,1,1,2,5,1,1,1,1,2,6,1,1,1,1,2,8,1,1,1,1,2,15,1,1,1,2,2) 

clec <- c(1, 1, 5, 5, 5, 1, 5, 5, 5, 5)

# Test statistic of ratio of variances with p-value

var_clec <- var(clec)

var_ilec <- var(ilec)

n_1 <- length(clec)

n_2 <- length(ilec)

observed_test_statistic <- var_clec / var_ilec

pf(observed_test_statistic, n_1 - 1, n_2 - 1, lower.tail = FALSE)```

Suppose that Verizon wishes to compare the variability of repair times for ILEC and CLEC customers. Consider the null hypothesis $H_0$: the population variance

of ILEC equals the population variance of CLEC.  Further, consider the teststatistic $F$ = (sample variance of CLEC) / (sample variance of ILEC).

This statistic follows an F distribution with degrees of freedom equal to(sample size of CLEC - 1) and (sample size of ILEC - 1). For these data the statistic for comparing the sample ratio of variances is 1.15 and the corresponding p-value is 0.34. The p-value of this test is very sensitive to the assumption that both populations are normally distributed. A viable alternative that does not depend on the assumption of normality is a permutation test. To compare this F-test and permutation test do the following:

+ Perform a one-sided permutation test on the ratio of variances. What is the p-value and what does it tell you?

+ What does a comparison of the two p-values say about the validity of the F   test for these data?

## ACT

You are trying to decide between two ACT prep classes. Class 1 begins with a general overview followed by an extensive number of practice exams. Class 2covers each topic in-depth with practice questions arranged by topic. Sample data for each class is available in the file `act.txt` in your RStudio CloudProject. You can read this data into R using `read.table("act.txt", header =TRUE)`. Based on a permutation test with 10,000 replications, does Class 1increase ACT scores on average? Answer the same question for Class 2?  Write a script named `act. R` or `act. Rmd` to address these questions. Underneath your code, write a conclusion as to which class (or, neither class) you would recommend. Justify your answers.

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