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What is the relationship between the empirical rule and a 95% confidence interval?
In Lesson 2 you first learned about the Empirical Rule which states that approximately 95% of observations on a normal distribution fall within two standard deviations of the mean. Thus, when constructing a 95% confidence interval your textbook uses a multiplier of 2.
Is margin of error always positive?
The margin of error is a statistic expressing the amount of random sampling error in the results of a survey. The margin of error will be positive whenever a population is incompletely sampled and the outcome measure has positive variance, which is to say, the measure varies.
How do you solve an Empirical Rule problem?
Solving Empirical Rule Questions
- Draw out a normal curve with a line down the middle and three to either side.
- Write the values from your normal distribution at the bottom.
- Write the percents for each section (you will need to memorize them!)
- Determine the section of the curve the question is asking for and shade it in.
What is the Empirical Rule for a normal curve?
The Empirical Rule states that 99.7% of data observed following a normal distribution lies within 3 standard deviations of the mean. Under this rule, 68% of the data falls within one standard deviation, 95% percent within two standard deviations, and 99.7% within three standard deviations from the mean.
What does 95% mean in the empirical rule?
The 95% for a confidence interval is a separate issue. A 95% confidence interval means that, if you took new samples from your population over and over, if you follow the procedure to calculate a 95% confidence interval, 95% of calculated confidence intervals will contain the true population value.
What is the 95% confidence interval of two standard deviations?
The 95% confidence interval is (1.8, 2.2). Please note that we talked in terms of 95% confidence using the empirical rule. The empirical rule for two standard deviations is only approximately 95% of the probability under the normal distribution.
How to calculate the 95% confidence level?
To calculate the exact 95% confidence level we would use 1.96 standard deviations. The 95% confidence interval implies two possibilities. Either the interval (1.8, 2.2) contains the true mean μ, or our sample produced an x ¯ that is not within 0.2 units of the true mean μ.
Where does the 2 in the 95% rule come from?
Recall the formula you used: The 2 in this formula comes from the normal distribution. According to the 95% Rule, approximately 95% of a normal distribution falls within 2 standard deviations of the mean.