Q1.
An administrator wanted to study the utilization of long-distance telephone service by a department. One variable of interest (let’s call it X) is the length, in minutes, of long distance calls made during one month. There were 40 calls that resulted in a connection. The length of calls, already ordered from smallest to largest, are presented in the following table.
A) (5 marks) Find the 5-number summary of X distribution.
B) (2 marks) Find mean and SD of X distribution.
C) (1 mark) Find the 4th Quintile (or the 80th percentile) of SD of X distribution.
D) (2 marks) Find the percentile rank of 8.6 minutes (X18).
STAT 203 HW Assignment 1 Q1. An administrator wanted to study the utilization of long-distance telephone service by a department. One variable of interest (let’s call it X) is the length, in minutes, of long distance calls made during one month. There were 40 calls that resulted in a connection. The length of calls, already ordered from smallest to largest, are presented in the following table. A) (5 marks) Find the 5-number summary of X distribution. B) (2 marks) Find mean and SD of X distribution. C) (1 mark) Find the 4th Quintile (or the 80th percentile) of SD of X distribution. D) (2 marks) Find the percentile rank of 8.6 minutes (X18). Q2. (This continues Q1) A) (4 marks) Use R to produce a histogram of the data in Q1. The observations should be broken down into 7 intervals of equal width specified in the following frequency distribution: The first class interval: [0.0 , 10.0) The second class interval: [10.0 , 20.0) The third class interval: [20.0 , 30.0) The fourth class interval: [30.0 , 40.0) The fifth class interval: [40.0 , 50.0) The sixth class interval: [50.0 , 60.0) The seventh class interval: [60.0 , 70.0] B) (2 marks) Describe the shape of the histogram. C) (4 marks) Use R to construct a boxplot and write down outliers of X distribution. Q3. Download the attached files, and make the following graphs: A) (5 marks) Make a histogram to show the weight distribution of the STAT 270 class. B) (5 marks) Make a bargraph to show the favorite color distribution of the STAT 270 class. Q4 Do Exercise 1.40 (page 43, textbook) Marijuana and traffic accidents. Part (a) 5 marks, Part (b) 5 marks. Q5 Part (a) 2 marks, Part (b) 2 marks, Part (c) 3 marks, and Part (d) 3 marks. Do Exercise 2.32 (page 69, textbook) Maternal age at Childbirth. Q6 Do Exercise 3.44 (page 97, textbook) Grading Managers. Q7. The scores on the Wechsler Adult Intelligence Scale are approximately Normal with μ = 100 and σ = 15. Find the shortest interval that covers 90% of WAIS scores. Q8. Osteoporosis is a condition in which the bones become brittle due to loss of minerals. To diagnose osteoporosis, an elaborate apparatus measures bone mineral density (BMD). BMD is usually reported in standardized form. The standardization is based on a population of healthy young adults. The World Health Organization (WHO) criterion for osteoporosis is a BMD 2.5 STANDARD DEVIATIONs below the mean for healthy young adults. BMD measurements in a population of people similar in age and sex roughly follow a Normal distribution. Women aged 60-70, of course, not young adults. The mean BMD in this age is about -1.0 on the standard scale for young adults. Suppose the standard deviation is the same as for young adults. What percent of this older population have osteoporosis? Q9. The average score of a statistics midterm exam was about 55, the SD was about 15, and the lowest score was 40. Did the exam scores follow the normal cure? Explain clearly. Q10. Do Exercise 4.28 (page 120, textbook) Ebola and gorillas. Part (a) 4 marks, Part (b) 3 marks, and Part (c) 3 marks Use R to generate the scatterplot in Part (a).