Mastering One Sample T-Interval: Guidelines To Accurately Estimate Population Mean

One Sample T-Interval for Population Mean CONDITIONS

x̄ ± t* (Sx/√n)df = n-1

In order to use a one sample t-interval to estimate the population mean, the following conditions must be met:

1. Random Sampling: The data should be collected using a random sampling method. This means that every individual in the population has an equal chance of being selected.

2. Normality: The sample data should follow a normal distribution. This means that the shape of the sample data should be bell-shaped, with most of the data around the mean and fewer data points further away from the mean. If the sample size is large enough (typically n > 30), this condition can be assumed based on the Central Limit Theorem.

3. Independence: Each observation in the sample should be independent of any other observation. This means that the outcome of one observation does not affect the outcome of any other observation.

If these conditions are met, then a one sample t-interval can be used to estimate the population mean with a certain level of confidence. The confidence level can be chosen by the user and determines the width of the interval, with higher confidence levels resulting in wider intervals.

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