A hospital emergency room (ER) has collected a sample of n = 40 to estimate the mean wait time in the ER. It has found the population standard deviation is 32. Using a 90 percent confidence level, what is its margin of error?

Question

BlackTom AI · Accepted Answer

We start by identifying the formula for the margin of error when estimating a population mean with a known standard deviation: ME = z * (sigma / sqrt(n)).

First, determine the z-critical value for a 90% confidence level. The 90% two-tailed interval leaves 5% in each tail, so z ≈ 1.645.

Next, note the given values: sigma = 32 and n = 40. Compute the standard error: sigma / sqrt(n) = 32 / sqrt(40).

Calculate sqrt(40) ≈ 6.3249, so 32 / 6.3249 ≈ 5.059.

Now multiply by the z-critical value: 1.645 * 5.059 ≈ 8.32.

Thus the margin of error is about 8.32, which rounds to approximately ±8.3 visits.

Option by option analysis:
- Option 1: Approximately ±8.3 visits — This matches the computed ME (≈8.32). It is correct.
- Option 2: Approximately ±1.5 visits — This is far smaller than the calculated margin; it would imply either a much smaller standard error or a smaller z-value, which is inconsistent with the given data.
- Option 3: About ±1.3 visits — Similar issue as Option 2; the margin is not close to 1.3, indicating a miscalculation of standard error or z-score.
- Option 4: About ±9.9 visits — This is larger than the computed ME (≈8.32) and would overstate the uncertainty; it suggests overestimating either z or sigma relative to n.

In summary, the precise computation using the standard formula with the supplied sigma, n, and confidence level yields a margin of error around 8.32, aligning with Option 1.

A hospital emergency room (ER) has collected a sample of n = 40 to estimate the mean wait time in the ER. It has found the population standard deviation is 32. Using a 90 percent confidence level, what is its margin of error?单项选择题

类似问题

位置5的问题 As the sample size increases, the margin of error decreases.TrueFalse

位置4的问题 If the margin of error in an interval estimate of μ is 3.8, the interval estimate equals 1.9 (that is half of 3.8).TrueFalse

A 96 % confidence interval for a mean was constructed. The confidence interval is as follows 6.1 ± 3.5 . What is the margin of error? Recall: a confidence interval is computed using 𝑥 ¯ ± 𝐸 . c07.p061.q025

What is the margin of error? Remember to use the same standard error you calculated in Question 7.24.

What is the margin of error?

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