4.18 Problem Set: Statistics

The instructions are as follows: Create three vectors of numbers. For each, print the vector, the mean, the median, the variance, and the standard deviation. Vector 1 should have the mean and median equal. Vector 2 should have the mean greater than the median. Vector 3 should have the mean less than the median. Use R to solve each of the following problems. The head of quality control stops by a factory to inspect the next 20 widgets produced. Over the past six months, 98% of widgets have passed inspection. What is the probability that less than 10 widgets pass inspection? The average test score in a large college statistics course with multiple sections is 85 and the standard deviation is five points. If you choose a student at random, what is the probability that their score is between 80 and 85? Over the past three years at the farm you manage, the watermelons average about nine pounds each with a standard deviation of two pounds. What is the probability that a watermelon randomly selected from your harvest will weigh more than 10 pounds? You manage a help desk. 90% of your tickets are resolved with the first reply. If you randomly select 10 tickets for review, what is the probability that all 10 were resolved with the first reply? From the MASS package, import the dataset “immer.” Read the documentation and describe the dataset in your own words. Is this data tidy? If not, tidy it and print the tidy dataset. Save your tidy dataset in a variable and work with it through the rest of the problem set. Use any tools that you like in R to answer the following questions. What values are present in the location variable? How many rows are there for each value? What values are present in the variety variable? How many rows are there for each value? How many years are represented in the dataset? How many rows are there for each year? What is the mean yield? What is the first quartile, median, and third quartile for yield? What are the minimum and maximum values for yield? What are the variance and standard deviation for yield? Create two boxplots for yield. The first boxplot should have bars that extend from the minimum to the maximum. The second boxplot should have bars that extend from (Q1 - 1.5 x IQR) to (Q3 + 1.5 x IQR). From the MASS package, import the dataset “Pima.tr.” Read the documentation and describe the data in your own words. Is the data tidy? If not, tidy it. Write a loop that calculates and prints the mean of each numeric variable.