s= 2.36 n= 350 confidence level 99%

mondidomarilyn31

mondidomarilyn31

Answered question

2022-04-19

s= 2.36 n= 350 confidence level 99%

Answer & Explanation

RizerMix

RizerMix

Expert2023-04-28Added 656 answers

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:
x¯±zα/2sn
where x¯ is the sample mean, zα/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:
zα/2=z0.0052.576
We can find the sample mean by dividing the sum of the sample values by the sample size:
x¯=i=1nxin
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:
x¯=s=2.36
Substituting these values into the formula for the confidence interval, we get:
2.36±2.5762.363502.36±0.433
Therefore, the length of the confidence interval is approximately 2(0.433)0.866.
In conclusion, the length of the confidence interval is approximately 0.866.

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