Biostats SDS 328M Homework 3 Part 1 - Hand work (all work must be done by hand). Write your answers onto one or more separate sheets of paper....

Copyright © 2016 Dept. of Statistics and Data Sciences, UT Austin Biostats SDS 328M Homework 3 Part 1 – Hand work (all work must be done by hand). Write your answers onto one or more separate sheets of paper. Clearly mark each sheet with your name and your lab time. Round all answers to at least 3 decimal places. 1. A new screening test has been developed to detect HIV infections. For people with HIV, the test has a 96% chance of detecting it (a positive test result). For people who do not have HIV, the test correctly produces a negative test result 83% of the time. Assuming that 4% of a population is infected with HIV, what is t he probability that someone who gets a positive test result is actually infected with HIV? Show all of your work for full credit. (4pt) 2. A peach farmer has two different varieties (named V ariety A and Variety B) of peach trees on her land . Twenty percent of her trees are V ariety A peaches and the other 80% are Variety B peaches . The weight s of Variety A peaches are normally distributed with a mean of 92 grams and a standard deviation of 8 grams . The weights of Variety B peaches are normally distributed with a mean of 103 grams and a standard deviation of 13 grams . a. What proportion of Variety A peaches weigh between 100 and 110 grams? (2pt) b. What weight of a Variety B peach corresponds to the third quartile of the distribution ? (2pt) c. Overall, what proportion of her peaches weigh less than 100 grams ? ( 4pt) d. If you randomly select a peach that weighs more than 100 grams , what is the probability that it was a Variety A peach ? ( 4pts ) Copyright © 2016 Dept. of Statistics and Data Sciences, UT Austin Part 2 – R work (must be done in R) Copy and paste your R code and output into a word document to submit to Canvas. Follow the se instructions to import the necessary data set:  Before opening the dataset needed for this problem , you’ll need to install and open the “car” package . Simply run the following two lines of code : > install.packages('car' ) > library(car)  Now you can import the “ Friendly” dataset and use it to answer the question below . Name the data frame with your UT EID: > my_eid < - Friendly 3. The Friendly dataset contains data from an experiment where participants had to recall words under one of three different conditions. The condition variable lists the condition (SFR, Before, or Meshed) the participant was under and the correct variable indicates how many words the participant recalled correctly. a. What is the overall mean and standard deviation of the number of correct words recalled by participants (regardless of condition) ? (1pt) b. Which condition had the highest mean number of words correct? Use logical indexing to find the mean number of correct words for each condition to answer this question. Be sure to include your code and output in your submission . (3pt)