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

Exhibit 10-10 provides the following data:

Product A: Shoppers Surveyed = 800, Shoppers Favoring This Product = 560 
Product B: Shoppers Surveyed = 900, Shoppers Favoring This Product = 612

We are asked for the standard error of p̂1 − p̂2, where p̂1 is the sample proportion for product A and p̂2 is the sample proportion for product B.

Option 1: 52
This value would be a large standard error for a proportion difference and does not align with the scale of typical standard errors, which are fractions, not whole numbers. It is not plausible given the sample sizes and proportions here.

Option 2: .044
To get .044, one would need a larger combined variability or a smaller denominator effect. Computing the actual standard error with the given data yields about 0.0225, not 0.044, so this overestimates the true standard error.

Option 3: None of the other three
This option would be correct only if none of the other numerical choices matches the computed standard error. Since one option (.0225) does match the calculation, this option is incorrect.

Option 4: .0225
This is the correct magnitude for the standard error of the difference in sample proportions. The formula is SE(p̂1 − p̂2) = sqrt[ p̂1(1 − p̂1)/n1 + p̂2(1 − p̂2)/n2 ].

Now, perform the calculation step by step to verify:
- p̂1 = 560/800 = 0.70, so p̂1(1 − p̂1) = 0.70 × 0.30 = 0.21; divide by n1 = 800 to get 0.21/800 = 0.0002625.
- p̂2 = 612/900 ≈ 0.68, so p̂2(1 − p̂2) = 0.68 × 0.32 = 0.2176; divide by n2 = 900 to get 0.2176/900 ≈ 0.0002418.
- Sum these: ≈ 0.0002625 + 0.0002418 ≈ 0.0005043.
- Take the square root: sqrt(0.0005043) ≈ 0.02246, which rounds to 0.0225.

Therefore, the standard error of p̂1 − p̂2 is approximately 0.0225, making option 4 the correct choice.

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 _____.单项选择题

类似问题

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.