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.

Question

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.

BlackTom AI · Accepted Answer

This item asks you to report the upper limit of the confidence interval for a difference of proportions, and it emphasizes that you should use a difference of proportions (not percentages).

Key idea to apply: when comparing two proportions p1 and p2 from independent samples with sizes n1 and n2, the standard error for the difference p1 - p2 is SE = sqrt[ p1(1 - p1)/n1 + p2(1 - p2)/n2 ].

Then, for the chosen confidence level (commonly 95%), the upper limit of the confidence interval for the difference is:
Upper limit = (p1 - p2) + z*SE,
where z is the critical value from the standard normal distribution (for 95% CI, z ≈ 1.96).

Important details to keep in mind:
- You must use the actual difference of proportions, not a difference of percentages. If p1 and p2 are expressed as proportions (e.g., 0.30 and 0.20), their difference is 0.10; if you mistakenly treat them as percentages (30% and 20%), you would get a different, incorrect scale.
- You need the observed proportions and the corresponding sample sizes to compute SE. Without the raw data (p1, p2, n1, n2), the numeric upper limit cannot be computed.
- If the problem specifies a different confidence level (e.g., 99%), use the corresponding z value (e.g., 2.576 for 99%).

In this particular prompt, the provided answer is 0.047. To determine whether that value is correct, you would substitute the actual observed p1, p2, n1, n2 into the formula above, compute SE, then compute (p1 - p2) + z*SE with the appropriate z for the intended CI. If your data yield a different observed difference or SE, the upper limit will change accordingly.

If you have the underlying data (p1, p2, n1, n2) or the observed difference and CI width, I can walk you through the exact calculation step by step and confirm whether 0.047 is the correct upper limit for your scenario.

MAST90007_2025_WIN 2025 Quiz 2

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.

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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 _____.

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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MAST90007_2025_WIN 2025 Quiz 2

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.

查看解析

登录即可查看完整答案

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 _____.

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 _____.

更多留学生实用工具

希望你的学习变得更简单

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 _____.