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What can we conclude with confidence intervals?
If a 95% confidence interval includes the null value, then there is no statistically meaningful or statistically significant difference between the groups. If the confidence interval does not include the null value, then we conclude that there is a statistically significant difference between the groups.
How can confidence intervals be used to make decisions?
Confidence intervals (CIs) provide a range of plausible values for a population parameter and give an idea about how precise the measured treatment effect is. CIs may also provide some useful information on the clinical importance of results and, like p-values, may also be used to assess ‘statistical significance’.
What are some limitations of confidence intervals?
It does not strictly express the probability that the interval in question contains the population mean, as this must be either 0% or 100%. The population mean is either included or not included. The function of a CI, therefore, is essentially an inferential one.
When do you use confidence intervals in statistics?
We can also make interval estimates (e.g., we are 95% confident that the interval (2.0 cm, 5.0 cm) covers the population mean). And this is where confidence intervals come in! Remember, every time we sample from a population, the values in the sample are likely to shift because of the random process of sampling.
Which is an alternative approach to statistical inference?
An alternative approach to statistical inference, using confidence intervals (CIs), assists in addressing some of these limitations.
How to calculate confidence intervals for the central limit theorem?
Using the population distribution we used to demonstrate the Central Limit Theorem, we will now sample (size n = 60) 100 times from this distribution and calculate 100 distinct confidence intervals (95%). How many confidence intervals would be expect to cover the true population mean (μ=2.25)?
What is the 95 percent confidence interval for mpg?
After the first 100 times he filled up the tank, he found the mean was 23.4 miles per gallon (mpg) with a population standard deviation of 0.9 mpg. Compute the 95 percent confidence interval for his mpg. 5. Which of the assumptions listed above might be problematic in making inference to the population in Question 4?