UTA BIOL 2300 - Complete Problems and Answers-2

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An Introduction to Biostatistics Third Edition Complete Problems and Answers Thomas Glover Hobart and William Smith Colleges Kevin Mitchell Hobart and William Smith Colleges c cid 13 1999 2015 by Thomas Glover and Kevin Mitchell This material may be reproduced for classroom use with the text An Introduction to Biostatistics Third Edition published by Waveland Press Please do not post this material on the internet For all other uses please obtain written permission of the authors 1 17 30 46 57 61 78 110 146 173 198 230 Contents 1 Problems and Answers 2 Problems and Answers 3 Problems and Answers 4 Problems and Answers 5 Problems and Answers 6 Problems and Answers 7 Problems and Answers 8 Problems and Answers 9 Problems and Answers 10 Problems and Answers 11 Problems and Answers Guide to Hypothesis Testing i Chapter 1 Problems and Answers 1 1 If X1 9 X2 8 X3 13 X4 6 and X5 9 evaluate the following cid 88 cid 88 cid 88 n cid 88 i 1 a Xi b Xi d g Xi X 2 i cid 80 Xi 2 X 2 n e h X 2 i Xi 9 i 2 4 cid 88 cid 88 cid 88 cid 88 c f Xi X cid 17 2 Xi i Xi 2 cid 88 cid 16 cid 88 3 cid 88 cid 88 i 1 j 5 k 2Xi l 2 Xi 1 The solutions are a 45 g 26 b 27 h 36 c 0 i 36 d 26 j 25 e 431 f 2025 k 90 l 90 2 The poison dart frog Dendrobates auratus is native to Costa Rica and other areas of Central and South America They were introduced to Hawaii and have ourished there These frogs concentrate toxins from their food and also modify various ingested compounds into toxins called allopumiliotoxins A small sample of these frogs was collected on Kauai Island and their overall lengths measured in cm The data appear below 4 1 5 2 4 3 5 1 4 7 4 5 3 9 4 6 4 3 For this sample nd the following a the sum of the X s b the sample mean c the uncorrected sum of squares d the corrected sum of squares e the standard deviation f the standard error g the range h Brie y discuss these measurements in light of the 30 300 rule 2 We nd cid 88 cid 88 a d Xi 40 7 cm Xi X 2 1 495556 cid 88 b X 4 52 cm c X 2 i 185 55 e s 0 43 cm f SE 0 14 cm g 1 3 cm h The range is 1 3 cm with 13 units tenths of centimeters between the largest and smallest values The 30 300 rule is therefore violated here The data should be measured to one more decimal place 1 2 CHAPTER 1 Problems and Answers 3 The red tailed tropic bird Phaethon rubricauda is an extremely rare sea bird that nests on several islands of the Queensland coast of Australia As part of a conservation e ort to manage these endangered birds every nesting pair was measured and weighed Below are the body weights of these birds in kg Female Male 2 45 2 86 2 57 2 65 2 81 2 75 2 37 2 60 2 01 2 30 2 50 2 49 2 32 2 84 a Determine the following descriptive characteristics for the weights of the females mean variance and standard deviation Is this a sample or population Again pay attention to number of decimal places and appropriate units b Determine the mean variance and standard deviation for the male weights c Comment on the di erences or similarities between the two data sets 3 a This is a population problem not a sample F 2 433 kg 2 F 0 0516 kg2 and F 0 227 kg b m 2 641 kg 2 c Females in general are slightly smaller and more variable than males m 0 0343 kg2 and m 0 185 kg 4 As part of a larger study of the e ects of strenuous exercise on human fertility and fecundity the ages in years of menarche the beginning of menstruation for 10 Olympic female endurance athletes runners and swimmers who had vigorously trained for at least 18 months prior to menarche were recorded 13 6 13 9 14 0 14 2 14 9 15 0 15 0 15 1 15 4 16 4 a Calculate the following descriptive statistics sample mean variance standard deviation and median b Do you feel that the sample mean is signi cantly higher than the overall population mean for non athletes of 12 5 years Provide a rationale for your answer 4 a Sample mean 14 75 yr variance 0 703 yr2 standard deviation 0 84 yr median 14 95 yr b The di erence between the claimed mean 12 5 yr and the sample mean 14 75 yr is 2 25 yr or approximately 2 7 standard deviations Is this a large distance We will consider methods to evaluate this distance in Chapter 3 Also no value in the sample is as low as the claimed mean The mean appears signi cantly higher for the female endurance athletes 5 Beetles of the species Psephenus herricki have an aquatic larval stage called water pennies Below are the overall lengths mm of a sample of water pennies collected from a stream owing into Seneca Lake in Geneva NY Calculate the sample mean variance standard deviation standard error median and range 8 1 7 9 8 3 7 2 6 8 7 0 7 3 8 5 6 8 6 3 7 0 7 5 7 3 8 4 6 9 5 5 7 3 7 7 6 8 6 8 5 9 8 0 8 2 8 6 7 4 5 The basic summary statistics are n 25 X 7 34 mm s2 0 64 mm2 s 0 80 mm SE 0 16 mm M 7 3 mm range 3 1 mm CHAPTER 1 Problems and Answers 3 6 In a study to determine the distribution of Cepaea nemoralis snails at the Hanley Wildlife Preserve in upstate New York 100 sampling quadrats were surveyed with the results in the table below Calculate the mean median and variance of the number of snails per quadrat in this study Note The corrected sum of squares is 345 No of snails Xi fi fiXi fiX 2 i 6 X 0 7 snails quadrat X 0 snails quadrat and s2 3 48 snails quadrat 2 7 In a new reality television program called Solitary Survivor 15 volunteers were placed in isolation chambers without clocks electronic devices or any other means of measuring time After a week their individual daily sleep cycles day lengths were measured and are recorded below Day lengths hr 26 0 25 3 25 5 26 1 26 5 25 9 24 3 25 4 24 2 26 2 26 5 25 1 27 4 27 1 26 6 a Calculate the mean and variance for this sample b Do you …


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