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What are the assumptions underlying the use of the t distribution in testing hypothesis about the...

What are the assumptions underlying the use of the t distribution in testing hypothesis about the population mean?

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The first assumption made regarding t-tests concerns the scale of measurement. The assumption for a t-test is that the scale of measurement applied to the data collected follows a continuous or ordinal scale, such as the scores for an IQ test.

The second assumption made is that of a simple random sample, that the data is collected from a representative, randomly selected portion of the total population.

The third assumption is the data, when plotted, results in a normal distribution, bell-shaped distribution curve.

The fourth and final assumption is a reasonably large sample size is used. A larger sample size means the distribution of results should approach a normal bell-shaped curve.

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