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.
​(Round to four decimal places as​ needed.)

Answer 1

To find the 95% confidence interval for the difference between two population proportions, calculate the sample proportions, determine the standard error of the difference, and then use the Z-score to find the margin of error. Add and subtract this from the difference in sample proportions.

Step-by-step explanation:

To find a 95% confidence interval for the difference between two population proportions, we use the formula:

CI = (p1 - p2) ± Z* √[(p1(1-p1)/n1) + (p2(1-p2)/n2)]

Where p1 and p2 are the sample proportions, n1 and n2 are the sample sizes, and Z* is the Z-score corresponding to the desired confidence level.

For this situation:

• p1 = 117/230
• p2 = 178/270
• n1 = 230
• n2 = 270
• Z* for 95% confidence is approximately 1.96

We calculate the confidence interval step by step:

1. Compute the sample proportions: p1 = 117/230 and p2 = 178/270.
2. Insert these values and the sample sizes into the formula.
3. Calculate the standard error of the difference in proportions.
4. Multiply this by the Z-score for the desired confidence level.
5. Add and subtract this value from the difference in sample proportions to obtain the confidence interval.

After performing these calculations, we will have the confidence interval for the difference between the two population proportions.