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# T-test for one sample Mean with critical values Calculator

Note: This calculator is for testing using sample mean and sd. If you only have sample values use ONE SAMPLE TEST FROM SAMPLE VALUES calculator

Population Mean: One tailed Two tailed

## You can see a sample solution below. Enter your data to get the solution for your question

$$\displaylines{---}$$
$$\displaylines{ \mathbf{\color{Red}{Left\;tail\;test}} \\ \\ \\ \\ \bar{x} = 22.3 \\ \\ \mu = 24.0 \\ \\ s = 2 \\ \\ n = 34 \\ \\ \alpha = 0.05 \\ \\ df=n-1= 34 -1 \\ \\ \Rightarrow 33 \\ \\ critical\;value\;z\;=\;\;\mathbf{\color{Red}{-1.69236}} \\ \\ H_{0}: \mu = 24.0 \\ \\ H_{a}: \mu < 24.0 \\\;\\\;Formula\;for\;test\;statistic\;t\;is \\ \\ t= \frac{\bar{x} - \mu }{\frac{s }{\sqrt{n}}} \\ \\ \\ So, t = \frac{22.3-24.0}{\frac{2}{\sqrt{34}}} \\ \\ \Rightarrow \frac{-1.7}{0.342997} \\ \\ \Rightarrow -4.956312 \\ \\ test\;statistic\;= \mathbf{\color{Red}{-4.956312}} \\ \\ p= 1e-05 \\ \\ p\;is\;less\;than\;\alpha\;.\; So,\;Reject\;H_{0} }$$