Question

The percentage of an ocean population that has sharks is unknown, so a simple random sample of 220 species is selected from the ocean. From the sample, 37 of the species were sharks. If we use the sample proportion as an estimate for the success probability for the population, what is the standard error associated to a sample of size 40 using this estimate? Round your answer to 4 decimal places.

Answer 1

It is given that in a sample of 220 species, 37 of the species were Sharks. So, the sample proportion of Shark is p

p=37/220=0.1682

The proportion of shark in a sample will follow Binomial distribution since if we use the sample proportion as an estimate for the success probability for the population then, Probability of success=p=0.1682

We know that the standard error is the standard deviation of statistics based on the sample.

So, standard deviation of the proportion of shark in the sample of size 40=√40*0.1682*(1-0.1682) = √5.59635=sqrt(5.59635) =  2.365661~ 2.3657

Thus, the standard error associated with a sample of size 40 using this estimate is 2.3657