Simple R Studio Homework Assignment Help

Simple R Studio Homework Assignment Help

 
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Book Homework 1. For a standard normal random variable (i.e, for a Z ∼ N(µ = 0, σ = 1) find the following: (a) P(Z < 1.2) (b) P(Z > −2.3) (c) P(−1 < Z < 0.31) (d) The 97.5 th percentile. 2. Assume that heart rate (in beats per minute, or bpm) for STA 100 students is distributed normal, with a mean of 110 bpm and a standard deviation of 20.2 bpm. Assume all students in the following problem are selected from this population. (a) Find the probability that a randomly selected students heart rate is above 125. (b) What percentage of randomly selected students could we expect to have a heart rate between 90 and 130? (c) What is the first and third quartile of heartrates for randomly selected students? (d) What is the 8th percentile for heart rates among randomly selected students? 3. The heights of men in a certain population follow a normal distribution with mean 69.7 inches and standard deviation 2.8 inches. (a) If 10 men are selected at random, what is the probability their average height is above 72 inches? (b) If exactly one man is selected at random, what is the probability his average height is above 72 inches? (c) What is the 80th percentile for the average height of 10 men? (d) What is the probability the average height of 10 men is between 70 and 71 inches? 4. Over 9 months, a random sample of 100 women were asked to record their average menstrual cycle length (in days). The sample average was 28.86 days, with a sample standard deviation of 4.24 days. (a) Calculate the 90% confidence interval for the true average menstrual cycle length. (b) Interpret the confidence interval found in (a) in terms of the problem. (c) A researcher hypothesized that womens menstrual cycles are typically the same length as a lunar month - 29.5 days. Does your interval from (a) support this hypothesis? Explain. (d) List two hypothetical ways we could reduce the width of this confidence interval. 5. Continue with the data from Problem 4. (a) If we wanted our confidence interval to have a margin of error of 0.5 days at 90% confidence, how many women should we sample (at least)? (b) If we wanted our confidence interval to have a margin of error of 0.1 days at 90% confidence, how many women should we sample (at least)? (c) What tends to happen to the sample size we need as the margin of error decreases? Explain based on (a) to (b), or in plain English. (d) What tends to happen to the sample size we need as the standard deviation increases? Explain. 16. Two treatment costs for a particular medical issue are being compared. The average cost of 210 randomly selected subjects for treatment A was $490, with a standard deviation of $32. The average cost for 180 randomly selected subjects for treatment B was $500, with standard deviation $48. Assume the d.f = 300. (a) Find the 99% confidence interval for the difference costs. (b) Interpret your interval from (a) in terms of the problem. (c) Does your interval suggest that the costs are different? Explain. (d) If we increased the confidence level (i.e, (1−α)100%), would the new interval be wider or narrower than that found in (a)? Explain (you do not need to calculate the interval). 7. Two baby-food manufacturers are competing, and manufacturer of brand A believes that their brand causes more weight gain in infants than manufacturer of brand B. A sample of size 15 fed their babies brand A for two months, and saw an average weight gain of 36.93 ounces, with a standard deviation of 4.23 ounces. A sample of size 25 fed their babies brand B and saw an average weight gain of 31.36 ounces with a standard deviation of 3.35 ounces. Assume the d.f. = 24. (a) Create a 95% confidence interval for the difference in weight gain between the two baby food brands. (b) Interpret your interval from (a) in terms of the problem. (c) Does your interval suggest one brand of baby food causes more weight gain than the other? Explain. (d) If the sample sizes increased to 100, but everything else remained constant, would our interval widen or narrow? Explain. 2R Homework Due electronically, on Friday, July 12th by 5pm. I. On Canvas you will find the file student.csv. It contains information on 1548 introduction to statistics students, and has the following columns: Column 1: height: The height of the student. Column 2: hsGPA: The high school GPA of the student. Column 3: pulse: The pulse rate of the student when measured in class. (a) Find the mean, and standard deviation of the column height in this dataset. (b) Use (a) to find the proportion of observations within 2 standard deviation of the mean. Print this proportion. Based on your result, does this suggest students heights are approximately normally distributed? Explain. (c) Plot a QQ plot (normal probability plot). Does this suggest students heights are approximately normally distributed? Explain. (d) Using R, find the 95% confidence interval for the average students height, and report it. II. Use the data from Problem I. (a) Plot a histogram of the column hsGPA. Does this data appear to be normally distributed? Explain. (b) Using R, find the 90% confidence interval for the average students high school GPA, and report it. (c) Interpret your interval from (b) in terms of the problem. (d) Did you need to assume that students high school GPA was normally distributed for your confidence interval to be valid? Explain why or why not. III. You will be using the dataset Radish.csv, which contains the growth rate of radish plants two weeks after germination. The first column is the height of the plants (in cm). The second column is the treatment group, which was either given no fertilizer (the control group) or given fertilizer (the treatment group). Assume the radishes were sampled randomly and independently. (a) Find the 95% confidence interval for this data, and interpret it in terms of the problem. (b) The fertilizer manufacturer claims that by using their fertilizer, plants will grow 1cm more on average than if you use no fertilizer. Does your confidence interval support this claim? Explain. (c) What is the largest difference in growth you could expect with 95% confidence, based on your confidence interval? Be specific about which difference you are looking at.



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