Exhibit 10-10
The results of a recent poll on the preference of shoppers regarding two products are shown below.

Product

Shoppers Surveyed

Shoppers Favoring
This Product

A

800

560

B

900

612

Refer to Exhibit 10-10. The standard error of is _____.

Question

Exhibit 10-10
The results of a recent poll on the preference of shoppers regarding two products are shown below.

Product

Shoppers Surveyed

Shoppers Favoring
This Product

A

800

560

B

900

612

​

Refer to Exhibit 10-10. The standard error of  is  _____.

BlackTom AI · Accepted Answer

Let’s break down what’s being asked and compute carefully.
First, determine the sample proportions for each product: for A, p1 = 560/800 = 0.70; for B, p2 = 612/900 = 0.68.
Next, the question asks for the standard error of the difference in proportions, p1 − p2. The formula is SE(p1 − p2) = sqrt[ p1(1 − p1)/n1 + p2(1 − p2)/n2 ].
Compute each term inside the square root:
- For product A: p1(1 − p1) = 0.70 × 0.30 = 0.21, and n1 = 800, so 0.21/800 = 0.0002625.
- For product B: p2(1 − p2) = 0.68 × 0.32 = 0.2176, and n2 = 900, so 0.2176/900 ≈ 0.000241777...
Add these two contributions: 0.0002625 + 0.000241777... ≈ 0.000504277...
Now take the square root: sqrt(0.000504277...) ≈ 0.02246.
Rounding to four significant figures gives about 0.0225.

Evaluating the answer choices:
- None of the other three: This would be chosen if none of the numbers matched, but we’ve calculated a value near 0.0225, so this seems unlikely.
- .0225: This matches the computed standard error value, given standard rounding.
- .044: This is roughly double the computed value and does not reflect the plus of two small variance components; it overestimates SE(p1 − p2).
- 52: This is an implausible value for a standard error in a proportion context and likely a distractor.

In summary, after applying the standard error formula to the two sample proportions and their respective sample sizes, the calculation yields a result around 0.0225, which aligns with the option labeled ".0225".

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Exhibit 10-10 The results of a recent poll on the preference of shoppers regarding two products are shown below. Product Shoppers Surveyed Shoppers Favoring This Product A 800 560 B 900 612 Refer to Exhibit 10-10. The standard error of is _____.

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