Estimate the mean number of absences per tutorial over the past 5 years with 90% confidence. The results were =11.6 and s=4.1 absences. Example:Ī random sample of 225 1st year statistics tutorials was selected from the past 5 years and the number of students absent from each one recorded. If sample size is less than 30 then we use t-distribution. If sampling without replacement, then needs to be n 30).Independence: Sampled observations must be independent.In fact, since this method is based on CLT it follows the same conditions for CLT. Some conditions need to be satisfied to use the above formula and to build the confidence interval. Conditions for confidence interval for Population mean In a confidence interval, z × SE is called the margin of error. Similarly, we can construct 90% and 99% confidence interval using above z critical value. If the interval spreads out 2 standard errors from the point estimate, we can be roughly 95% confident that we have captured the true parameter: point estimate ± 2 × SE. The standard error represents the standard deviation associated with the estimate, and roughly 95% of the time the estimate will be within 2 standard errors of the parameter. Since n is large the unknown σ can be replaced by the sample value s. The sample standard deviation (s) provides an estimate of the population standard deviation (σ). However, most of the time when the population mean is being estimated from sample data the population variance is unknown and must also be estimated from sample data. A plausible range of values for the population parameter is called a confidence interval. Instead of giving just a point estimate of a parameter, it would be better to provide a range of values for the parameter. However, a point estimate is not perfect and usually there is some error in the estimate. A point estimate gives a single value for a parameter. So, a Confidence Interval is an interval of numbers containing the most plausible values for our Population Parameter. A confidence interval provides a range of values that is likely to contain the true population average with a certain level of confidence (such as 95% or 99%). However, this sample average may not be exactly equal to the true population average. It is commonly used in statistics to estimate the unknown population parameter (such as the mean or the proportion) based on a sample of data.įor example, if you want to estimate the average height of all people in a certain country, you can take a sample of people and calculate their average height. A confidence interval is a range of values that is likely to contain the true value of a population parameter with a certain degree of confidence.
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