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Confidence Intervals Calculator

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Example
Created on 2024-06-20Asked by Aria Martin (Solvelet student)
Calculate a 95% confidence interval for the mean of a sample with xˉ=50 \bar{x} = 50 , s=10 s = 10 , and n=25 n = 25 .

Solution

Step 1: Identify the sample mean xˉ=50 \bar{x} = 50 , sample standard deviation s=10 s = 10 , and sample size n=25 n = 25 . Step 2: Calculate the standard error of the mean: SE=sn=1025=105=2. \text{SE} = \frac{s}{\sqrt{n}} = \frac{10}{\sqrt{25}} = \frac{10}{5} = 2. Step 3: Find the critical value for a 95% confidence interval. For a normal distribution, z=1.96 z = 1.96 . Step 4: Calculate the margin of error: ME=z×SE=1.96×2=3.92. \text{ME} = z \times \text{SE} = 1.96 \times 2 = 3.92. Step 5: Compute the confidence interval: CI=xˉ±ME=50±3.92. \text{CI} = \bar{x} \pm \text{ME} = 50 \pm 3.92. Step 6: Conclusion. The 95% confidence interval for the mean is (46.08,53.92) (46.08, 53.92) . Solved on Solvelet with Basic AI Model
Some of the related questions asked by Layla Robinson on Solvelet
1. Construct a 95% confidence interval for the population mean based on a sample of 50 observations with a sample mean of 25 and a population standard deviation of 52. What is the sample size needed to create a 99% confidence interval for the mean with a margin for error of 2 given a population standard deviation of 10?
DefinitionConfidence intervals are a type of statistical interval, were developed to estimate the range in which a population parameter, such as the mean or proportion, lies with a particular confidence level llikelihood is likely to fall. They are prepared using a set of data samples and give a range of likely values for a population parameter and a level of confidence. These confidence intervals are then are employed in inferential statistics to make inferences about population parameters and to give an indication of their uncertainty. Illustration:A 95% confidence interval for the population mean µ from the sample of mean xˉ and standard deviation s would be given by xˉ±1.96n​s​where n is the sample size.
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