Question

LC50 for a chemical is the lethal concentration for 50% of animals or humans. For example, if water contains a chemical at the LC50 concentration, 50% of the fish population in the water would die. Environment Canada collects data on LC50 concentrations. Suppose a random sample of 60 perch (a type of fish) gives a mean LC50 for DDT of 17 parts per million and a standard deviation of 5 parts per million.

(a) Find a 95 % confidence interval for the true mean LC50. (b) What is the margin of error?

Answer 1

answer)

to find the confidence interval, we need to determine the margin of error

the margin of error is = z*standard error

standard error is = standard deviation/ square root of n

n = 60

standard deviation is = 5

so standard error = 6/ square root of 60 = 0.77459666924

now the value of z for 95% confidence interval is 1.96

therefore,

margin of error = 1.96*0.77459666924

= 1.51820947171

now, the confidence interval is given by

mean - margin of error to mean + margin of error

given mean is 17

so required confidence interval is

[ 17-1.51820947171, 17+1.51820947171]

[15.481790528, 18.51820947171]