Question

1. Suppose we go back to the example from question 3. Suppose the probability remains at 16% but we now take a sample of size 100.
   1. What is the standard error of the proportion?
   2. What is the probability that the sample proportion of people who have white as ethnicity is between 10% and 25%?
2. Two estimates are available for the same population parameter. Estimate one has a standard deviation of 9.3 and estimate two has a standard deviation of 9.4. Estimate two is unbiased, whereas estimate one is biased. Which estimate would you choose and why?

Answer 1

Answer)

Given n = sample size = 100

P = 0.16 (16%)

Now first we need to check the conditions or normality that is if n*p and n*(1-p) both are greater than 5 or not

N*p = 16

And N*(1-p) = 84

As both are greater than 5, conditions are met and we can use standard normal z table to estimate the answers

A)

Standard error is = √{p*(1-p)}/√n

= 0.03666060555

B)

We need to find

P(10<x<25)

P(0.1<x<0.25)

= p(x<0.25) - p(x<0.1)

P(x<0.25)

Z = (x-mean)/s.E = (0.25-0.16)/0.03666060555

Z = 2.45

From z table, p(z<2.45) = 0.9929

P(x<0.1)

Z = (0.1-0.16)/0.03666060555

Z = -1.64

From z table, P(Z<-1.64) = 0.0505

Required probability is 0.9929-0.0505 = 0.9424