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Why mean of the population is known but standard deviation is unknown ? Mean is calculated from individual values then why can't standard deviation be calculated? Is there any practical scenario where mean is known but standard deviation is unknown?

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    $\begingroup$ It is a test about the mean: one specific value of the mean is tested as being compatible (or not) with the sample. The true mean is unknown, like the standard deviation. $\endgroup$ – Xi'an Nov 26 '15 at 17:35
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Your premise is incorrect.

The mean of the population is NOT known in a t test. You hypothesize a mean (or mean difference) for the population. When comparing two groups, this is usually zero. When comparing one sample of data against an ideal population, the population mean is hypothesized. Then you compute the mean and SD of the sample, and compute the t ratio (t statistic) and complete the t test.

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  • $\begingroup$ I think I should have written t stat. I will confirm and correct the question. Thanks for pointing it out. $\endgroup$ – Siddhesh Nov 26 '15 at 17:46

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