s= 2.36 n= 350 confidence level 99%

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RizerMix · Accepted Answer

We are given that the sample standard deviation is

s = 2.36

, the sample size is

n = 350

, and the confidence level is 99%. We need to find the length of the confidence interval.
The formula for the confidence interval is:

\bar{x} \pm z_{α / 2} \frac{s}{\sqrt{n}}

where

\bar{x}

is the sample mean,

z_{α / 2}

is the critical value of the standard normal distribution for a given confidence level

α

,

s

is the sample standard deviation, and

n

is the sample size.
For a 99% confidence level, the value of

α

is 1% or 0.01. The critical value of the standard normal distribution for a 99% confidence level and a two-tailed test is:

z_{α / 2} = z_{0.005} \approx 2.576

We can find the sample mean by dividing the sum of the sample values by the sample size:

\bar{x} = \frac{\sum_{i = 1}^{n} x_{i}}{n}

However, we are not given the sample values, so we cannot compute the sample mean. Instead, we will use the worst-case scenario to find the maximum length of the confidence interval.
The worst-case scenario occurs when the sample mean is equal to the sample standard deviation. In this case, we have:

\bar{x} = s = 2.36

Substituting these values into the formula for the confidence interval, we get:

2.36 \pm 2.576 \frac{2.36}{\sqrt{350}} \approx 2.36 \pm 0.433

Therefore, the length of the confidence interval is approximately

2 (0.433) \approx 0.866

.
In conclusion, the length of the confidence interval is approximately 0.866.

s= 2.36 n= 350 confidence level 99%

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