Question

Consider the following results for independent samples taken from two populations.

Sample 1	Sample 2
n1 = 500	n2= 200
p1= 0.42	p2= 0.31

a. What is the point estimate of the difference between the two population proportions (to 2 decimals)?

b. Develop a 90% confidence interval for the difference between the two population proportions (to 4 decimals). Use z-table.
to

c. Develop a 95% confidence interval for the difference between the two population proportions (to 4 decimals). Use z-table.
to

Answer 1

(a) The best point estimate of the difference between the two population proportion is the , i.e. ,

So, the difference of the two sample population proportion serves the best point estimate of the difference between the two population proportions.

(b) The confidence interval for the two population proportion is calculated as-

Since, we have to construct a 90% confidence interval.

So, for 90% confidence interval,

and

                                                                               

                                                                                

                                                                                

                                                                                 

So, the 90% confidence interval for the difference of population proportion is calculated as

(c) Calculation for the 95% confidence interval for the difference in population proportion is calculated as-

For 95% confidence interval ,

                                                                               

                                                                               

                                                                              

                                                                               

So, the 95% confidence interval for the population proportion of difference of proportion is calculated as