1. Most penguin species are not sexually dimorphic, which means they lack obviou
ID: 2935941 • Letter: 1
Question
1. 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 be the proportion of females in the population. (a) Compute a numerical point estimate of . (b) Compute the estimated standard error of your estimate. (c) Is it reasonable to compute a 95% CI for using the normal approximation in this case? If it is possible, explain why, and make the CI. If it is not possible, explain why.
Explanation / Answer
Given that n=20
In which 12 males and 8 females
a) Point estimate of
= 8/20 =0.4
b) Given that Standard error = (1 - ) / n
= 0.4*0.6/20
= 0.012
=0.1095
c) To calculate 95 % confidence interval for P
± z * (1 - ) / n
= 0.4 ± 1.96*0.1095
=0.4± 0.2146
=0.1854,0.6146
Yes it is possible to calculate
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