Part B

Complete the following questions using R and R commander.

1. Young children need calcium in their diet to support the growth of their bones. A study examined whether or not a sample of children consumed an adequate amount of calcium. Since there are different requirements for children at different ages, the children were classified into three age groups: Group 1 (3-6 years), Group 2 (7-10 years), Group 3 (11-13 years). There were 1000 children in the study. The dataset "Calcium.xlsx" contains the findings.

a) Complete the contingency table by hand and then check your answer by generating a two-way table in R.

Use the frequency table from (a) estimate the following probabilities.

b) Find the probability that a randomly selected child is 3-6 years old.

c) Find the probability that a randomly selected child is 11-13 years old and consumed an adequate amount of calcium.

d) Find the probability that a randomly selected child is 7-10 years old or consumed an adequate amount of calcium.

e) Find the probability that a randomly selected child that didn't consume enough calcium is 11-13 years old. That is, find the probability that a randomly selected child is 11-13 years old, given they didn't consume enough calcium.

f) Find the probability that a randomly selected 11-13 years old child didn't consume enough calcium.

g) Are events N and G3 independent? Explain your answer.

h) Are events A and G3 mutually exclusive? Explain your answer.

Question 2 uses the data set "Insurance.xlsx," which contains information regarding 1338 policy holders of an insurance company; download this data set and use R commander to complete the following tasks. For each question, copy or take a screenshot of the output in R commander and submit it with your solutions to each question. To save space, you only need to copy and paste what is asked for in the questions and should adjust the size of the image when appropriate.

2. Use R commander to obtain the most appropriate table to answer the following questions. Hint: construct a frequency distribution in part (a), and contingency tables in parts b through f.

a) If we randomly select a policy holder, what is the probability that they are a smoker?

b) If we randomly select a policy holder, what is the probability that they are a female and a smoker?

c) If we randomly select a female, what is the probability that she is a smoker?

d) If we randomly select a non-smoker, what is the probability that they are a male and from the southwest?

e) If we randomly select a policy holder, what is the probability they live in the southwest or are a smoker, given they are male?

f) If we randomly select a male smoker, what is the probability that he is from a southwest region.

3. Recall from part A that Courtney makes 65% of her free throws. she attempts 100 free throws.

a) What is the probability that she will miss at most 40 of them?

b) What is the probability that she will miss at least 20 of them?

c) What is the probability that the number of throws that she will miss is at least 25 and at most 35?