Question

A company that advertises on the Web wants to know which search engine its customers prefer as their primary search engine: Google or Bing. Specifically, the company wants to know whether the preference depends on the browser being used. The file P08_28.xlsx contains counts of 800 customers' favorite search engine, broken down by the browser used.

Round your answers to three decimal places and if your answer is negative value, enter "minus" sign.

a. Calculate a 95% confidence interval for the difference between two proportions: the proportion of Internet Explorer users whose favorite search engine is Google and the similar proportion of Firefox users

Favorite search engine	Internet Explorer users	Firefox users	Other browser users	All users
Google	192	211	31	434
Bing	161	131	22	314
Other	27	18	7	52

Answer 1

Favorite search engine	Internet Explorer users	Firefox users	Other browser users	All users
Google	192	211	31	434
Bing	161	131	22	314
Other	27	18	7	52
Sum	380	360	60	800

We need to construct the 95% confidence interval for the difference between population proportions P1 P2. We have been provided with the following information about the sample proportions Favorable Cases 1 (X1)- 192 380 211 360 Sample Size 1 (Ni) Favorable Cases 2 (X2)- Sample Size 2 (M) = The sample proportion 1 is computed as follows, based on the sample size N, = 380 and the number of favorable cases Xi 192: Xi192 P N - 380 0.505 The sample proportion 2 is computed as follows, based on the sample size N2 number of favorable cases X2 211: 360 and the X2 211 2360 0.586 The critical value for α 0.05 is computed as shown below: = Z-a/2-1.96. The corresponding confidence interval is

CI (ea 0.505(1- 0.505) 0.586(1-0.586) = 10.505 0.586-1.96× 0.505(1- 0.505) 0.586(1-0.586) 380 360 380 360 (-0.152,-0.009) Therefore, based on the data provided, the 95% confidence interval for the difference between the population proportions Pi-P2 is-0.152 < p <-0.009, which indicates that we are 95% confident that the true difference between population proportions is contained by the interval (-0.152, -0.009)