What value of z should you use for a 99% confidence interval for the difference of two population proportions?

Question

BlackTom AI · Accepted Answer

To determine the z value for a 99% confidence interval for the difference of two population proportions, we need the critical z* value that corresponds to a two-tailed alpha of 0.01 (since 99% confidence leaves 1% in each tail).

Option by option analysis:

- Option 1: 2.58
  This value is the commonly used critical z* for a 99% two-sided confidence interval. Since 99% confidence implies 0.01 in each tail, the standard normal critical value that cuts off 0.005 in the upper tail of the standard normal distribution (and 0.005 in the lower tail) is approximately 2.58. This matches the standard z-table lookup for 99% confidence.

- Option 2: 2.33
  A z* of 2.33 corresponds to roughly a 98% confidence interval (two-tailed), where the total alpha is about 0.02 (0.01 in each tail). Therefore 2.33 is not appropriate for 99% confidence.

- Option 3: 3.08
  A z* around 3.08 would correspond to a much higher confidence level, well above 99%. This value is typically associated with confidence levels around 99.8% or more, depending on the exact tail probabilities, so it overstates the needed critical value for 99%.

- Option 4: 2.75
  A z* of 2.75 aligns more with a confidence level near 99.1% to 99.2% depending on the precise tail probabilities, but it is not the standard z* used for exactly 99% confidence. It is not the conventional value associated with 99%.

In summary, the 99% two-sided confidence interval requires the critical z* that leaves 0.005 in each tail, which is approximately 2.58. The other values correspond to different (lower or higher) confidence levels and do not match the 99% criterion.

What value of z should you use for a 99% confidence interval for the difference of two population proportions?单项选择题

类似问题

If we change a 95% confidence interval estimate to a 90% confidence interval estimate, we can expect the _____.

The expression used to compute an interval estimate of μ may depend on any of the following factors EXCEPT _____.

A 97% confidence interval for the difference 𝜇 1 − 𝜇 2 is (4.2, 5.8). If you were to change the confidence level to 93% instead, which of the following could represent a plausible interval?

Which of the following results in a wider confidence interval? Assume the sample proportion stays the same.

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单