STAT 2507 Assignment # 1 (Chapters 1, 2 and 3) Winter 2015

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 clickingon Graph histogram(b) [2] Circle the shape of the frequency histogram of the data. Skewed to the leftSymmetricalSkewed to the right(c) [2] What is the relationship between the mean and the median of this data set?1(d) [2] Now activate the command mode by clicking Editor Enable Commands. Usethe command desc for the column (Histogram) data. The mean is – andthe median is(e) [2] Would you use Chebychevs 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 litergasoline.(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 canbe 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 andbody 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 theBrain weight.(c) [2] Use the preceding regression line to predict the Brain weight of an specie with Bodyweight=110.(d) [2] What is the equation of regression line when the Brain weight is used to predict theBuddy weight.(e) [2] Predict the Body weight of a mammal specie with Brain weight=5.2Part II Comprehension questions1. 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 themedian value.(b) [2] Compute the z-score for the observation 10. Would you consider this value as anoutlier? 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 postalmailings by a company. Leaf Unit = 0.0185 2868788899091 3 4 892 0 0 1 393 1 1 2 5 794 0 1 6 6 7 8 995 2 3 4 5 596 0 597 0 4 79899100 03(a) [4] What are the values of the median, lower quartile (Q1), and upper quartile (Q3) forthis data set?(b) [8] Construct a box plot for the given data. Using the 1.5*IQR rule, list any potentialoutliers, if any.4. [5] A company interested in lumbering rights for a certain tract of slash pine trees is told thatthe mean diameter of these trees is 35 cm with a standard deviation of 7 cm. Assuming thedistribution of diameters is roughly symmetrical and bell-shaped, what percent of the treeswill have diameters between 21 and 49 centimeters?5. We have n = 1000 measurements whose mean and variance respectively, are x = 6 and S 2 = 9.(a) [5] What is the minimum number of measurements that lie inside [0, 12]. Indicate thenumber and explain how it was obtained.(b) [5] If you know that the shape of the distribution of the measurements is bell-shapedand 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 necessarycatheter length and the patients height measured.Patient12345678910Height (in inches)42.863.537.539.545.538.54322.53723.5Catheter Length (centimeters)37503436432837203430(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.