Study Guide for MT1
Study Guide for MT1 Biology 1114
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This 5 page Study Guide was uploaded by an elite notetaker on Sunday October 4, 2015. The Study Guide belongs to Biology 1114 at Ohio State University taught by Dr. Robin Taylor in Fall 2015. Since its upload, it has received 32 views. For similar materials see Biology for the Life Sciences in Biology at Ohio State University.
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Date Created: 10/04/15
1 My neighbors believe that their cat Tootsie is leftpawed To test whether Tootsie actually has a preference for his left paw over his right paw we dangled a ribbon in his face and recorded which paw he used to bat at it We did this 10 times and he batted at the ribbon with his left paw 9 times and with his right paw once a Let the random variable X be the number of times Tootsie uses his left paw Assuming that he is equally likely to use either paw what is the distribution of X name it and give the values of its parameters b What are the mean and variance of X c Find the probability that Tootsie uses his left paw at least once d Find the probability that Tootsie uses his left paw exactly 5 times e Carry out an appropriate hypothesis test to examine whether Tootsie has a preference for using her left paw Make sure to follow the four steps introduced in class and to state your statistical and practical conclusions f Provide an interpretation of the pvalue you computed 2 In a certain community 8 percent of all adults over 50 have diabetes A health service in this community correctly diagnoses 95 percent of all persons with diabetes as having the disease and incorrectly diagnoses 2 percent of all persons without diabetes as having the disease Let D be the event that a randomly selected adult over 50 has diabetes and let G be the event that an adult over 50 is diagnosed as having diabetes Find the following probabilities a Draw an appropriate probability tree b NW C PGID d PGCID e PGnD f Find the probability that the community health service will diagnose an adult over 50 as having diabetes g Find the probability that a person over 50 diagnosed by the health service as having diabetes actually has the disease 3 Match each of the following summary statistics to one of the histograms below au340o20 bu340o50 cu300o20 Historam I Historam H llFreqwe nw Frequency 25 Ell quot 15 quot lll quot 24B 2630 23D Still 30 3 13910 Historam HI Freq LEEch 3i 25 quot Ell quot 15 quot lll quot 2m 360 4tm Sin 4 Suppose I randomly selected 10 males from our class and recorded their weight lbs to obtain the following data 135lbs 162bs129bs193bs 155lbs 172lbs 156lbs 162lbs 180lbs 183bs a Compute the sample mean b Compute the sample standard deviation c Compute the sample median d Compute the coefficient of variation e Draw a boxplot for this data f Based on the boxplot and the mean and median you computed is the distribution approximately symmetric left skewed or right skewed 5 A biologist wanted to know if the cowpea weevil has a preference for one type of bean over another as a place to lay eggs She put equal amounts of four types of seeds into a jar and added adult cowpea weevils After a few days she observed the following data Type of Bean Number of Eggs Pinto 150 Cowpea 176 Navy Beans 174 Northern Beans 214 Do these data provide evidence of a preference for one type of bean Carry out the appropriate statistical test Make sure to follow the four steps introduced in class and to state your statistical and practical conclusions 6 Consider a discrete random variable with the following probability mass funcUon PXx 38 14 18 14 aFind PXlt3 bFind PXgt1 c Find the mean of X dFind the variance of X 7 Consider a continuous random variable X with the following probability dens yfuncUon fx38x2 0ltxlt2 and fx0 otherwise aShow that fx is a pdf bCacuate PX13 c Calculate PO5ltxlt1 8 What is the law of total probability What does it mean for two events to be independent What does it mean for two events to be mutually exclusive 9 Let PA 02 PB 05 and PA o B 06 a Find PAC b Find PAnB c Find PAB d Are A and B independent Justify your answer 10 Suppose we are interested in nding out whether a die is biased We toss the die 300 times and observe the following data Number on Die Times Rolled 59 42 45 46 52 OWU39lbULJNl l 56 Do these data provide evidence that the die is biased Carry out the appropriate statistical test Make sure to follow the four steps introduced in class and to state your statistical and practical conclusions 12 In Ohio 45 of all households have at least one pet Also if a household has at least one pet the chance that children are part of the household is 87 If a household does not have pets the chance that children are not part of the household is 75 Answer the following questions based on this scenado aDraw an appropriate probability tree bWhat is the probability that a household has at least one pet and children cWhat is the probability that there are children in the household dGiven that the household has no pets what is the probability that they have children eGiven that a household has children what is the probability they have no pets 13 Horses are helpful animals but they can be dangerous if poorly cared for In the 19th century the then Prussian army kept track of the number of fatalities caused by horsekicks to members of 10 of their cavalry regimens over a 20year timespan If the deaths occurred independently with equal probability then they should follow a Poisson distribution If some of the regiments were particularly bad horsemen the events would not occur with equal probability so the data would not follow Poisson Conduct a test on the following data Number of Number of Deaths X regiment years 0 109 1 65 2 22 3 3 4 1 gt4 0
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