In a survey conducted by a business management company, 51% of the U.S. workers siad they have negotiated a pay raise at least once inthier lives. The sample size used in the study was not disclosed. A) Suppose that the survey had a sample size of n=500. Construct a condifidence interval estimate for the proportion of all United States workers who have negotiated a pay raise. Solution Answer to the question) P = 0.51 n = 500 Standard error SE = srt(0.51 *0.49/500) SE = 0.0224 . Let the confidence level = 95% , so the Z critical value = 1.96 . The formula of cofndience interval is: p - z* SE , p + z * SE . On plugging the values we get 0.51 - 1.96 *0.0224 , 0.51 +1.96 *0.0224 0.04661 , 0.5539.

1. In your own words discuss the following.
1. Briefly describe the process of speciation, and define allopatric speciation?
2a. Differentiate between exponential and logistic growth curves?
2b. Give examples of the conditions under which each would occur?
Solution
1.Speciation can be defined as the formation of new species.Speciation is the evolutionary
process by which a species splits into two or more species.The process of speciation occurs in
four step.
Step 1 : Variation,one population one species.
Step 2 : Isolation,two population one species.
Step 3 : Selection,two Subspecies one species.
Step 4: Speciation,two species.
The four geographic modes of speciation are,Allopatric,Paraptric,Sympatric,Peripatric.
Allopatric speciation : Allopatric speciation is the differentiation of physically isolated
population from its ancestors.
2a. Exponential growth occurs when a population grows at a constant rate, usually appears in J
shaped.Logistic growth occurs when population stops and following a period of exponential
growth., usually appears in S-shaped.