One Sample T-Interval for Population Mean CONDITIONS
x̄ ± t* (Sx/√n)df = n-1
Before discussing the conditions required for constructing a one sample t-interval for population mean, let’s first define what a one sample t-interval is.
A one sample t-interval is a confidence interval that estimates the true population mean for a single group of observations or data.
Now, there are certain conditions that need to be met in order to construct a one sample t-interval for population mean. These conditions are:
1) Independent observations – The observations or data should be collected independently from each other. This means that the value of one observation should not affect the value of another observation.
2) Normality – The population from which the sample is taken should be approximately normal. This means that the distribution of the data should be symmetric and bell-shaped.
3) Random sample – The sample should be chosen randomly from the population. This ensures that the sample is representative of the population and reduces bias in the results.
If these conditions are met, then a one sample t-interval for population mean can be constructed using the sample mean, sample standard deviation, sample size and the desired level of confidence.
It is important to note that if the sample size is less than 30, the distribution of the population doesn’t have to be normal but the samples should be taken from populations that are at least approximately normal. If the sample size is larger than 30, the central limit theorem ensures an approximately normal distribution of the sample mean.
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