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 isstudent submitted image, transcription available below. ≺ - px - py≻

Answer 1

To create a 95% confidence interval for the difference between two population proportions, Px and Py, calculate the sample proportions, determine standard error, and multiply by the Z-score for a 95% confidence level, which is typically 1.96. The resulting interval represents the range in which the true difference is likely to fall.

Step-by-step explanation:

When finding a 95% confidence interval for the difference between two population proportions (Px and Py), we use a formula that incorporates the sample proportions, sample sizes, and the Z-score for the specified confidence level. In this scenario, we are comparing the proportion of shoppers who check the price before putting a product in their cart for items at regular price versus items at special price.

To find the confidence interval, we calculate the sample proportions (p-hat) for both groups:

• For shoppers choosing regular priced products: p1 = 117/230
• For shoppers choosing special priced products: p2 = 178/270

Then, we calculate the standard error for the difference between the two proportions. Finally, we use the Z-score that corresponds with a 95% confidence interval (which is typically 1.96) to compute the margin of error. The confidence interval is thus calculated as (p1 - p2) ± Z * Standard Error.

The confidence interval will provide a range that we are 95% confident includes the actual difference between the two population proportions Px and Py regarding the behavior of checking prices before placing items in the cart.