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# We Helped With This R Language Programming Assignment: Have A Similar One?

Category | Programming |
---|---|

Subject | R | R Studio |

Difficulty | College |

Status | Solved |

More Info | Statistics Homework Help Online |

## Short Assignment Requirements

## Assignment Description

** **

**IE 200: Engineering Statistics**

**Computing Assignment 3**

**1.** Recall the following
question from our lecture:

A laboratory blood test is 95% effective in detecting a certain disease when it is, in fact, present. However, the test also yields a “false positive” result for 1% of the healthy people tested. (That is, if a healthy person is tested, then, with probability 0.01, the test will imply he or she has the disease.) If 0.5% of the population actually has the disease, what is the probability a person has the disease given that the test result is positive?

**a) **Write
a __function__ that gives the probability of interest for the given rates of
false positive, effectiveness and disease prevalence. Test your function to
make sure that you get the correct probability as we calculated in class, i.e.,
0.32.

myprob<-function(a,b,c) # This is the function that will calculate the probability of interest

{

(a*b)/((a*b)+(c*(1-b)))

}

answer1 <-myprob(a=0.95,b=0.005,c=0.01) # We use the function to find the answer

**b) **Use
the function in part (a) to plot the probability of interest for prevalence
levels 0—0.5, with the granularity (i.e., step size) of 0.001.
Use the command *plot* and draw a line by setting type="l".

What can you say about the probability of interest at different prevalence levels? Comment on your observation.

**c) **Additional
to the plot from part (b), **add** two **lines** of two different colors corresponding
to the probability of interest when:

1. The effectiveness is 97.5% (i.e., its original 5% error rate is reduced by 50%).

2. The false positive rate is reduced by 50% to 0.5%.

You can use the
command *lines*. Color line (1) in red and color line (2) in blue.

Which approach is more effective in improving the probability of interest for a low prevalence disease, (1) or (2) in part c above?

**2**.
Consider problem 5 from HW 5.

A shipment of 7 television sets contains 2 defective
sets. A hotel makes a random purchase of 3 of the sets. If *X *is the
number of defective sets purchased by the hotel, find the probability
distribution of *X*.

**a)** Write a generic __function__ in R that can calculate
the probability of interest for different values of X, for any number of good
television sets, n, any number of defective television sets, m, and any number
of sets that the hotel purchases, k. (For instance, in problem 5 from HW 5, n =
5, m = 2, k = 2 and hence for X = 1, the function needs to return 4/7.)

**b)** Use this function to find the expected value of
random variable X, if n = 8, m = 6, k = 3.