Full Question:.
Most penguin species are not sexually dimorphic, which means they lack obvious outward body characteristics which indicate sex. Observation of behavior or a blood test can determine Penguin sex. A penguin researcher is interested in estimating the proportion of females in a large penguin population. She takes a random sample of n = 20 penguins and determines the sex of each one using a blood test. She finds 12 males and 8 females. Let π be the proportion of females in the population.
(a) Find a point estimate of π.
(b) Find the estimated standard deviation of your estimate.
(c) Is it reasonable to compute a 95% confidence interval for π using the normal approximation in this case? If it is possible, explain why, and make the interval. If it is not reasonable, explain why.
a. The female penguins are 0.4 in proportion to the male.
b. Standard Error = 0.110
c. Yes, it is.
See Explanation
Step-by-step explanation:
Given
n = 20 penguins
m = Male = 12
f = Female = 8
π = the proportion of females in the population...
a. Calculating a point estimate of π.
This is calculated by dividing number of females by total penguins
π = f/n
π = 8/20
π = 0.4
So, the female penguins are 0.4 in proportion to the male.
b. Calculating Standard Error
Standard Error is calculated by √(pq/n)
Where p = 0.4 --- calculated above
q = 1 - p = 1 - 0.4
q = 0.6
n = 20
Standard Error = √(0.4*0.6/20).
Standard Error = 0.109544511501033
Standard Error = 0.110 -; Approximated
c. Checking Possibilities
Expected Value of Male = 20(0.6) = 12
Expected Value of Female = 20(0.4) = 8
20(0.4) and 20(0.6) are both greater than 5, so we can approximate the distribution as normal. The C sill be (0.18, 0.62).
