Question

Use R to do each of the following. Use R code instructions that are as general as possible, and also as efficient as possible. Use the Quick-R website for help on finding commands. 1. Enter the following values into a data vector named Dat: 45.4 44.2 36.8 35.1 39.0 60.0 47.4 41.1 45.8 35.6 2. Calculate the difference between the 2nd and 7th entries of this vector using only reference indices. 3. Calculate the median of Dat. 4. Sort the values in this data vector from highest to lowest, and save the sorted version as a vector named sortDat. 5. What does sortDat[-4] do ? 6. What does Dat[-c(2,7,9)] do ? Why do you think the c() function necessary here ? 7. Suppose a random variable X has a normal distribution with a mean of µ = 60 and a standard deviation of σ = 4. Find the following using R functions: a. The probability that X is less than or equal to 66. b. The probability that X is between 50 and 60. c. The probability that X is greater than 68. 8. Use the Dat data vector below to answer the following questions 45.4 44.2 36.8 35.1 39.0 60.0 47.4 41.1 45.8 35.6 a. Use logical referencing to calculate the standard deviation of only those values that are less than 45. b. Write an R command that will determine how many of the vector entries are less than 45. c. Write an R command that will determine how many vector entries are greater than 40 but less than 55 (i.e. how many entries are between 40 and 55). d. Write an R command that will calculate what proportion of the data vector has values exceeding 40. 9. This exercise uses an existing R data frame called cigsales that contains state-level data regarding cigarette sales and other variables. a. The variable black indicates the percentage of a given state that is African-American. Using logical referencing, select from this data frame only those states that have over a 15% African- American population. What states get selected ? b. Extract the variable price from this data frame, and place it into a vector of its own called price.vec. c. Use logical referencing to create two separate vectors

Answer 1

All R commands are shown in bold. The output of the R commands are shown in Italics.

1.

Dat = c(45.4, 44.2, 36.8, 35.1, 39.0, 60.0, 47.4, 41.1, 45.8, 35.6)

2.

Dat[2] - Dat[7]
[1] -3.2

3.

median(Dat)
[1] 42.65

4.

sortDat = sort(Dat, decreasing = TRUE)

5.

sortDat[-4]
[1] 60.0 47.4 45.8 44.2 41.1 39.0 36.8 35.6 35.1

It removes the fourth element from the sortDat vector.

6.

Dat[-c(2,7,9)]
[1] 45.4 36.8 35.1 39.0 60.0 41.1 35.6

It removes the second, seventh, ninth element from the Dat vector.

c() function necessary here because you want to remove more than one data present at different indexes.

7.

a. The probability that X is less than or equal to 66.

pnorm(66, mean = 60, sd = 4)
[1] 0.9331928

b. The probability that X is between 50 and 60.

pnorm(60, mean = 60, sd = 4) - pnorm(50, mean = 60, sd = 4)
[1] 0.4937903

c. The probability that X is greater than 68.

pnorm(68, mean = 60, sd = 4, lower.tail = FALSE)
[1] 0.02275013