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% CI for π using the normal approximation in this case? If it is possible, explain why, and make the CI. If it is not possible, explain why.

(d) Are the data strong evidence the population proportion of females is different from 63%? Run a test at level α = .05 to find out.

How do I do part d?

Answer 1

d)Here, we need to test,

H₀: p=0.63

Vs., H1: p0.63 (claim)

It is a two-tailed test.

Given that, x=8, n= 20 and p₀= 0.63,   = x/n =8/20=0.4

We will use z test,

and the test statistics is given by,

z= =  =-2.13

p value = 0.0331< 0.05(level of significance).

since, the p value is less than the level of significance, we reject the null hypothesis.

Yes, there is enough evidence to conclude that the population proportion of females is different from 63%.