## Go back to

.....The site is being constantly updated, so come back to check new updates.....

If you find any bug or need any improvements in solution report it here

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

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

Population Mean: 2, 4, 6, 7, 8 One tailed Two tailed

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

$$\displaylines{---}$$
$$\displaylines{First\;we\;have\;to\;find\;mean\;and\;sample\;standard\;deviation }$$
$$\displaylines{}$$
$$\displaylines{Mean = \frac{\sum_{i=1}^{n}x_{i}}{n} \\ \\ \,=\frac{2+4+6+7+8}{5} \\ \\ \,=\frac{27}{5} \\ \\Mean = 5.4 }$$
$$x$$
$$\bar{x}$$
$$x-\bar{x}$$
$$[x-\bar{x}]^{2}$$
$$2$$
$$5.4$$
$$-3.4$$
$$11.56$$
$$4$$
$$5.4$$
$$-1.4$$
$$1.96$$
$$6$$
$$5.4$$
$$0.6$$
$$0.36$$
$$7$$
$$5.4$$
$$1.6$$
$$2.56$$
$$8$$
$$5.4$$
$$2.6$$
$$6.76$$
$$Total$$


$$23.2$$
$$\displaylines{}$$
$$\displaylines{Sample \;variance = (\sigma)^{2} = \frac{\sum_{i=0}^{n}(x_{i}-\bar{x})^{2}}{n-1} \\ \\ \Rightarrow \frac{23.2}{4} \\ \\ \Rightarrow 5.8 \\ \\ \sigma = \sqrt{variance} \\ \\ \Rightarrow \mathbf{\color{Red}{2.408319}} }$$
$$\displaylines{}$$
$$\displaylines{\\ \\ Now\;we\;can\;start\;significant\;test \\ \\ }$$
$$\displaylines{}$$
$$\displaylines{ \mathbf{\color{Red}{Right\;tail\;test}} \\ \\ \\ \\ \bar{x} = 5.4 \\ \\ \mu = 5 \\ \\ s = 2.408319 \\ \\ n = 5 \\ \\ \alpha = 0.05 \\ \\ H_{0}: \mu = 5 \\ \\ H_{a}: \mu > 5 \\ \\ df=n-1= 5 -1 \\ \\ \Rightarrow 4 \\ \\ critical\;value\;t\;=\;\;\mathbf{\color{Red}{2.131847}} \\\;\\\;Formula\;for\;test\;statistic\;t\;is \\ \\ t= \frac{\bar{x} - \mu }{\frac{s }{\sqrt{n}}} \\ \\ \\ So, t = \frac{5.4-5}{\frac{2.408319}{\sqrt{5}}} \\ \\ \Rightarrow \frac{0.4}{1.077033} \\ \\ \Rightarrow 0.371391 \\ \\ test\;statistic\;= \mathbf{\color{Red}{0.371391}} \\ \\ p= 0.364591 \\ \\ p\;is\;more\;than\;\alpha\;.\; So,\;Failed\;to\;Reject\;H_{0} }$$
$$\displaylines{}$$
$$\displaylines{}$$