Question

- 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.
- What is the standard error of the proportion?
- What is the probability that the sample proportion of people who have white as ethnicity is between 10% and 25%?

- 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

6. Suppose we go back to the example from question 3. Suppose
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