The process by which a single species splits into two species is still not well understood. One hypothesis is that in species in which female mate more than once would be more prone to associate with sexual conflict and this conflict can lead to speciation. Research identified 25 insect groups (Taxon pair), in which one group the female mate multiple times, and the other closely related group the female only mate once. The results can be found in the table below.     Number of species     Taxon pair Multiple-mating group Single-mating group Difference Above (+) or below (-) zero A 53 10 43 + B 73 120 -47 - C 228 74 154 + D 353 289 64 + E 157 30 127 + F 300 4 296 + G 34 18 16 + H 3400 3500 -100 - I 20 1000 -980 - J 196 486 -290 - K 1750 660 1090 + L 55 63 -8 - M 37 115 -78 - N 100 30 70 + O 21000 600 20400 + P 37 40 -3 - Q 7 5 2 + R 15 7 8 + S 18 6 12 + T 240 13 227 + U 115 14 1 + V 77 16 61 + W 15 14 1 + X 85 6 79 + Y 86 8 78 + State your null and alternative hypotheses.                 Use binomial test to test the hypothesis. [hint: x= number of (-) n= total number of taxon pairs]                   Interpret the p-value and state the conclusion from your test

Spam Email Filters.  A study by Forbes indicated that the five most common words appearing in spam emails are shipping!, today!, here!, available,  and fingertips!.  Many spam filters separate spam from ham (email not considered to be spam) through application of Bayes' theorem.  Suppose that for one email account, 1 in every 10 messages is spam and the proportions of spam messages that have the five most common words in spam email are given below. shipping! 0.051 today! 0.045 here! 0.034 available 0.014 fingertips! 0.014 Also suppose that the proportions of ham messages that have these words are: shipping! 0.0015 today! 0.0022 here! 0.0022 available 0.0041 fingertips! 0.0011 a.  If a message includes the word shipping!, what is the probability the message is spam?  If a message includes the word shipping!, what is the probability the message is ham?  Should messages that include the word shipping! be flagged as spam? b.  If a message includes the word…

7. The simplest type of inheritance occurs when a trait is governed by a pair of genes, each of which may be of two types, say G and g. An individual may have a GG combination, or Gg (which is the same as gG), or gg. Often, the GG and Gg genotypes are indistinguishable in appearance, in which case we say that the G gene dominates the g gene. An individual is called dominant if they have GG genes, a hybrid if they have Gg genes, and recessive if they have gg. Consider a process of continued matings. We start with an individual whose genotype is known, and mate it with a hybrid. An offpsring is chosen at random and is mated with a hybrid. This process is repeated through a number of generations. The genotype of the chosen offpsring in successive generations can be represented by a Markov chain. The states are indicated by GG, Gg, and gg respectively. The stochastic matrix is: P = GG Gg 99 GG Gg 99 [0.5 0.25 0] 0.5 0.5 0.5 0 0.25 0.5 a) Suppose the process is started with a hybrid bred to…

25. An egg company is studying the effects of artificial lighting on egg production of chickens. A brood of chicks were separated at random into two groups, both raised in windowless coops with artificial lighting. One group followed a natural 24-hour per day light/dark cycle while the second group experienced an accelerated 20- hour day. The weekly egg productions for the two groups are summarized in the table below. Conduct a hypothesis test to determine whether egg production is higher with a 20-hour day as compared to a 24-hour day. The level of significance is 1%. Wnat is the conclusion of the hypothesis test? Sample size Mean number of eggs Standard Deviation 24-hour day (Group 2) 20-hour day (Group 1) 45 5.2 1.8 42 6.1 2.9 A. We have enough evidence to conclude that the sample mean egg production with artificial lighting at a 20-hour day is higher than that at a 24-hour day. B. We do NOT have enough evidence to conclude that the sample mean egg production with artificial…

The United States Bureau of Labor Statistics (BLS) conducts the Quarterly Census of Employment and Wages (QCEW) and reports a variety of information on each county in America. In the third quarter of 2016, the QCEW reported the total taxable earnings, in millions, of all wage earners in all 3222 counties in America. Suppose that James is an economist who collects a simple random sample of the total taxable earnings of workers in 56 American counties during the third quarter of 2016. According to the QCEW, the true population mean and standard deviation of taxable earnings, in millions of dollars, by county are ?=28.29 and ?=33.493 , respectively. Let ? be the total taxable earnings, in millions, of all wage earners in a county. The mean total taxable earnings of all wage earners in a county across all the counties in James' sample is ?⎯⎯⎯ . Use the central limit theorem (CLT) to determine the probability ? that the mean taxable wages in James' sample of 56 counties will be less than…

Juvenile long-tailed tits (Aegithalos caudatus), a European relative of the chickadee, “help" adult birds raise offspring, such as by feeding their nestlings. What is the evolutionary advantage of helping behavior: practice for parenthood; increased changes of inheriting the adults’ territory in future; or indirect genetic benefits via increased success of kin? To investigate, Russell and Hatchwell (2001) monitored the behavior of 17 juveniles, each of which lived equidistant from two nests of adult birds. In each case, one nest was parented by a relative of the helper, and the other was parented by non-kin adults. Sixteen of the juveniles helped at the nest of their kin, whereas one helped at the non-kin nest. Do these results provide evidence for preferential helping at the nests of kin? Conduct the appropriate test.