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. At 95% confidence for the interval estimation of P 1-P 2, the margin of error 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. At 95% confidence for the interval estimation of P 1-P 2, the margin of error is  _____.

BlackTom AI · Accepted Answer

First, I restate the question in my own words to focus on the calculation at hand: we are given two proportions from independent samples and asked for the 95% margin of error for the interval estimate of P1 - P2.
Option A: .044. To evaluate this, compute the standard error for the difference between two proportions: SE = sqrt( (p1 q1)/n1 + (p2 q2)/n2 ). Here, p1 = 560/800 = 0.70, q1 = 1 - p1 = 0.30, n1 = 800; p2 = 612/900 ≈ 0.68, q2 = 1 - p2 = 0.32, n2 = 900. Then (p1 q1)/n1 = (0.70 * 0.30)/800 = 0.21/800 = 0.0002625, and (p2 q2)/n2 = (0.68 * 0.32)/900 = 0.2176/900 ≈ 0.000241777... Summing gives ≈ 0.00050428. The standard error is sqrt(0.00050428) ≈ 0.02246. For a 95% confidence interval, use the z* value of approximately 1.96, so the margin of error is 1.96 * 0.02246 ≈ 0.04399, which rounds to 0.044. This aligns with option A, so option A matches the computed margin of error.
Option B: None of the other three. This would only be correct if none of the listed values matched the calculation. Since we just computed ≈ 0.044 and option A matches, this statement is incorrect.
Option C: .0225. The number 0.0225 would correspond to the standard error itself, not the margin of error, and it is approximately half of the actual margin of error we calculated (0.02246 vs 0.04399). Therefore, this value is not the margin of error and is not correct in this context.
Option D: .064. A margin of error of 0.064 would require a larger standard error or a larger z* than 1.96; given the calculated SE ≈ 0.02246, multiplying by 1.96 yields about 0.044, not 0.064, so this option overstates the margin of error.
In summary, option A reflects the calculated margin of error using the standard two-proportion SE formula with a 95% confidence level, while the other options either misstate the quantity (standard error vs. margin of error) or misapply the concept, or claim alternatives that are inconsistent with the computation.

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类似问题

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 _____.

Questions 8 and 9 continued: Report the upper limit of the confidence interval to three decimal places. Make sure your answer is a difference of proportions, not a difference of percentages.

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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类似问题

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 _____.

Questions 8 and 9 continued: Report the upper limit of the confidence interval to three decimal places. Make sure your answer is a difference of proportions, not a difference of percentages.

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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MGS2150W05 final- Requires Respondus LockDown Browser

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 _____.

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 _____.