Question

Supermarket shoppers were observed and questioned immediately after putting an item in their cart. Of a random sample of 230 choosing a product at the regular price, 117 claimed to check the price before putting the item in their cart. Of an independent random sample of 270 choosing a product at a special price, 178 made this claim. Find a 95% confidence interval for the difference between the two population proportions.

Let Px be the population proportion of shoppers choosing a product at the regular price who claim to check the price before putting it into their cart and let Upper Py be the population proportion of shoppers choosing a product at a special price who claim to check the price before putting it into their cart.
The 95% confidence interval is .
(Round to four decimal places as needed.)

Answer 1

To find the 95% confidence interval for the difference between the two population proportions, we can use the formula for the confidence interval. This will give us the range within which we can confidently estimate the difference between the two proportions.

Step-by-step explanation:

We are given two samples, one of 230 shoppers choosing a product at the regular price and another of 270 shoppers choosing a product at a special price. We also know that 117 shoppers from the regular price sample claimed to check the price, while 178 shoppers from the special price sample made this claim. To find the 95% confidence interval for the difference between the two population proportions, we can use the formula for the confidence interval:

CI = (p^x - p^y) ± z * sqrt((p^x * (1 - p^x) / nx) + (p^y * (1 - p^y) / ny))

Where p^x and p^y are the sample proportions, nx and ny are the sample sizes, and z is the z-score corresponding to the desired confidence level. Substituting the given values, we get:

CI = (117/230 - 178/270) ± 1.96 * sqrt((117/230 * (1 - 117/230) / 230) + (178/270 * (1 - 178/270) / 270))

Calculating this expression will give us the 95% confidence interval for the difference between the two population proportions.