Question

2. 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.

1. (a) Find a point estimate of π.

2. (b) Find the estimated standard deviation of your estimate.

3. (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.

4. (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.

Answer 1

a) The point estimate of proportion here is computed as:

b) The standard deviation of the estimate is computed here as:

Therefore 0.1095 is the estimate required here.

c) np = 8 < 10 and therefore it wont be a reasonable assumption that the sampling distribution of the proportion here is normal. Therefore the confidence interval cannot be obtained here.

d) For hypothesized proportion value of 0.63, the test statistic is computed here as:

The p-value is computed for this two tailed test as:

p = 2P( Z < -2.1305) = 2*0.0166 = 0.0332

As the p-value here is 0.0332 < 0.05 which is the level of significance, therefore the test is significant and we can reject the null hypothesis and conclude that the population proportion of females is different from 63%