STAT 2507 Assignment 1 | Complete Solution

STAT 2507 Assignment # 1 (Chapters 1, 2 and 3) Winter 2015
Last Name , First
Student:

Lab group: very important {
Due: Sections E, F and H, Monday February 9
Section G Tuesday February 10

The Assignments are to be handed IN CLASS. No late Assignment will be accepted.
No electronic submission will be accepted.

Part I. Lab questions. Use only the blanks left to answer lab questions.
1. (Students'Weights) Column Weights contains the weights (to the nearest tenth of a kilogram) of 30 students.
(a) [2] Construct a stem-and-leaf plot for the data by clicking Graph ! Stem-and-Leaf.
(b) [2] What is the median weights of the students? {
(c) [2] What fraction of weights below 60 kilograms?
(d) [2] What are the smallest and the largest weights? { and {
(e) [2] Quarter of the weights are above what value?

2. (Histogram Data)
(a) [2] Construct a frequency histogram for \Histogram.Data" in the data le by clicking on Graph ! histogram
(b) [2] Circle the shape of the frequency histogram of the data. Skewed to the left Symmetrical Skewed to the right
(c) [2] What is the relationship between the mean and the median of this data set?

(d) [2] Now activate the command mode by clicking Editor ! Enable Commands. Use the command desc for the column (Histogram) data. The mean is - and the median is
(e) [2] Would you use Chebychev's theorem or empirical rule for this data?
Explain

3. (Milage) The data in the column \Milage" are the milage in kilometers of 20 cars on one liter
gasoline.
(a) [2] Do you see any outliers? How many?
(b) [2] Look at the boxplot and at the measurements and List the value(s) you think can be outliers.{
(c) [2] Compute lower fence  and upper fence -
(d) [2] Compute lower fence  and upper fence
{
(e) [2] Compare your candidates for outliers in part (c) to the lower and the upper fence.
{

4. (Regression) The data in columns \Brain" and \Body" are averages of weights of brain and body weights of a number of mammal species.
(a) [2] Compute the correlation coecient between the Brain and the Body weights? {
(b) [2] What is the equation of regression line when the Body weight is used to predict the
Brain weight.{
(c) [2] Use the preceding regression line to predict the Brain weight of an specie with Body
weight=110.
(d) [2] What is the equation of regression line when the Brain weight is used to predict the
Buddy weight.
(e) [2] Predict the Body weight of a mammal specie with Brain weight=5.



Part II Comprehension questions
1. Identify each of the following variables as categorical, discrete, or continuous. Use space left.
(a) [2] Blood type for a randomly selected person. .
(b) [2] Amount of snow (in inch) of the next snow storm in Ottawa {.
(c) [2] Daily exchange rate of Canadian dollar versus US dollar{.
(d) [2] The number of car accidents in Ottawa area tomorrow {.

2. Consider the following observations 1, 0, 5, 10, -5, 3.
(a) [3] Compute x, the mean of these data, and S, the standard deviation, and nd the median value.
(b) [2] Compute the z-score for the observation 10. Would you consider this value as an outlier? Why or why not?

3. The following is a stem and leaf plot for data on the costs (in dollars) of a sample of 31 postal
mailings by a company. Leaf Unit = 0.01
85 2
86
87
88
89
90
91 3 4 8
92 0 0 1 3
93 1 1 2 5 7
94 0 1 6 6 7 8 9
95 2 3 4 5 5
96 0 5
97 0 4 7
98
99
100 0

(a) [4] What are the values of the median, lower quartile (Q1), and upper quartile (Q3) for this data set?
(b) [8] Construct a box plot for the given data. Using the 1.5*IQR rule, list any potential outliers, if any.

4. [5] A company interested in lumbering rights for a certain tract of slash pine trees is told that the mean diameter of these trees is 35 cm with a standard deviation of 7 cm. Assuming the distribution of diameters is roughly symmetrical and bell-shaped, what percent of the trees will have diameters between 21 and 49 centimeters?

5. We have n = 1000 measurements whose mean and variance respectively, are x = 6 and S2 = 9.
(a) [5] What is the minimum number of measurements that lie inside [0; 12]. Indicate the number and explain how it was obtained.
(b) [5] If you know that the shape of the distribution of the measurements is bell-shaped and symmetrical, then approximately how many measurements are in the interval [3; 9].
Indicate the number and explain how it was obtained.

6. For 10 young patients, catheters were fed from a principal vein into the heart. The necessary catheter length and the patients' height measured.
Patient 1 2 3 4 5 6 7 8 9 10
Height (in inches) 42.8 63.5 37.5 39.5 45.5 38.5 43 22.5 37 23.5
Catheter Length (centimeters) 37 50 34 36 43 28 37 20 34 30
(a) [5] Obtain the equation of the linear regression of Catheter Length on Height
(b) [5] Estimate the required Catheter Length for a patient whose Height is 36 inches.
(c) [5] Obtain the equation of the linear regression of Height on Catheter Length
(d) [5] Estimate the height of a patient who requires a Catheter with length 22 centimeters.