HP340: Statistical Methods, Spring 2015Due Date: 3:30PM, Tuesday Feb 3, 2015 Homework 2 Total Points: 40Instructions: Clearly circle the letter of the best answer for multiple-choice questions and show your work when calculations are required. Late assignments will not be accepted.1. (3 points) A study on the effects of meditation on blood pressure rates was conducted on a group of middle-aged nurses working more than 60 hours per week. The study found that after a 30-minute meditation session, a few nurses had very high blood pressure, but many more had low blood pressure. The frequency distribution of these scores would be _____. A. BimodalB. Positively skewedC. A rectangular distributionD. Negatively skewedE. A non-modal distribution2. (3 points) An examination that clearly distinguished between those students who knew the material and those who did not would most likely yield a _____ distribution. A. unimodalB. bimodalC. trimodalD. multimodalE. median3. (3 points) If the distribution of exam scores are negatively skewed, the mean will have a value _____ .A. higher than the median B. equal to the median C. lower than the median D. either higher or lower than the median, depending on the value of the modeE. None of the above4. (4 points) For each of the following statements, indicate the statistic described from the choices below. A. Mean B. Median C. Mode B. Also known as the 50th percentile. A. Considered the most useful measure of central tendency for inferential statistics. C. There may be more than one value, depending on the distribution. A. Would change most if an extreme value was added to the dataset. 5. (5 points) From choices A-F select the measure that matches the descriptionA. Range B. IQR (interquartile range) C. s (population standard deviation) D. s (estimated standard deviation) E.2s(population variance) F. s2 (estimated population variance) F It is the sum of the squared deviations from the sample mean divided by the number of scores minus one.D It is the square root of the sum of squared differences of each score from the mean of a sample divided by the sample size minus one. A Its value is the difference between the lowest and highest score in a distribution. B It provides an interval that contains the middle 50% of the scores in a distribution and is found by subtracting the 25th percentile score from the 75% percentile score.E Its value can be calculated by X −μ∑(¿)2Npop¿6. (11 points) In this exercise, false statements regarding interval/ratio variables are presented. You are required to construct a small dataset to show that the statement is false, along with a brief explanation of how you came up withyour counterexample. Below is an example of a false statement, a small dataset that shows that it is false., and a brief explanation of how the dataset was constructed.Example Statement: the mode is always smaller than mean. Counterexample: 0, 2, 2, 2 where mode=2 and mean=1.5 Explanation: Mode is the most frequently occurring score; it can be at any position of the dataset, including the largest/smallest. To show the statement is false, we construct a small dataset where the largest value occurs most frequently. Then the mode couldn't be smaller than the mean since the mean is no larger than the largest value. (Notice that a dataset where the mode is the smallest score would have worked as well, and many other less extreme configurations would also work.Important Since it's extremely rare that two independent individuals would come up with exactly the same dataset, duplicate answers will not be awarded credit a. (5 points) Statement: For any given dataset, median is sensitive to extreme scores. Counterexample: 2,4,5,6,7,8,9 median: 62,4,5,6,7,8,9,45 median:7Explanation: The median will only shift over one number left or right with an extreme outlier. The extreme outlier would have the same effect on the median as any other number added to the data set because it only causes the median to shift one number. The data sets above both have very similar medians but different means.b. (6 points) Statement: median is always between the mode and the mean. In other words, it's either: mode < median < mean or mean < median < mode. Counterexample: 2,4,5,20,20  Mode: 20, Median: 5, Mean: 10.2Explanation: When there are multiple extreme outliers, the mode and the mean are forced to favor those extreme numbers, while the median will still lie in the middle no matter what. The data used has small numbers close to eachother, and then two larger outliers that force the mode to be 20 and the mean to be 10.2, which is greater than the median, which remains 5 even if the two numbers above it were extreme or not.7. (11 points) The data provided in HP340 Homework2 Data.xls are the same 50 distances between gazelle and predator that we used in HW1. For these data: a) (8 Points) Find the median, mean, range, IQR, s2 and s. Median: 61Mean: (all numbers added divided by 50) 66.24Range: 205-18= 187IQR: 72-47= 25s2 (sample variance): S2=(X - X )2åNSample=XD2åNs2=(X - m)2åNPopulation = 1333.29s (estimated population standard deviation): 1N)XX(s2= 36.51b) (3 points) compare the median to the mean. What does the difference between the values tell you aboutthe shape of the distribution? The median (61) is smaller than the mean (66.24), so therefore the shape of the distribution wouldbe positively skewed and the tail would be on the