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Is it okay to use hypothesis testing with a t test when population distribution is not...

Is it okay to use hypothesis testing with a t test when population distribution is not normal? Provide the reason why.

Math   Statistics-And-Probability   
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No it is not Okay to use the hypothesis testing with a t test when population distribution is not normal, because for applying the t-test on the hypothesis, we need to assume that population is normally distributed.

The t-test assumes that the means of the different samples are normally distributed; it does not assume that the population is normally distributed. The t-test is invalid for small samples from non-normal distributions, but it is valid for large samples from non-normal distributions.

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