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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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Answer #1

(1)The first assumption made regarding t-tests concerns the scale of measurement.

(2)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.
(3) The third assumption is the data, when plotted, results in a normal distribution, bell-shaped distribution curve.
(4)The fourth 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.
(5)The final assumption is the homogeneity of variance. Homogeneous, or equal, variance exists when the standard deviations of samples are approximately equal.

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