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Crypto fear and greed index

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

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

$$ \displaylines{---} $$
$$ \displaylines{First\;we\;have\;to\;find\;mean\;and\;sample\;standard\;deviation } $$
$$ \displaylines{} $$
$$ \displaylines{Mean = \frac{\sum_{i=1}^{n}x_{i}}{n} \\ \\ \,=\frac{2+4+6+7+8}{5} \\ \\ \,=\frac{27}{5} \\ \\Mean = 5.4 } $$
$$ x $$
$$ \bar{x} $$
$$ x-\bar{x} $$
$$ [x-\bar{x}]^{2} $$
$$ 2 $$
$$ 5.4 $$
$$ -3.4 $$
$$ 11.56 $$
$$ 4 $$
$$ 5.4 $$
$$ -1.4 $$
$$ 1.96 $$
$$ 6 $$
$$ 5.4 $$
$$ 0.6 $$
$$ 0.36 $$
$$ 7 $$
$$ 5.4 $$
$$ 1.6 $$
$$ 2.56 $$
$$ 8 $$
$$ 5.4 $$
$$ 2.6 $$
$$ 6.76 $$
$$ Total $$
$$ $$
$$ $$
$$ 23.2 $$
$$ \displaylines{} $$
$$ \displaylines{Sample \;variance = (\sigma)^{2} = \frac{\sum_{i=0}^{n}(x_{i}-\bar{x})^{2}}{n-1} \\ \\ \Rightarrow \frac{23.2}{4} \\ \\ \Rightarrow 5.8 \\ \\ \sigma = \sqrt{variance} \\ \\ \Rightarrow \mathbf{\color{Red}{2.408319}} } $$
$$ \displaylines{} $$
$$ \displaylines{\\ \\ Now\;we\;can\;start\;significant\;test \\ \\ } $$
$$ \displaylines{} $$
$$ \displaylines{ \mathbf{\color{Red}{Right\;tail\;test}} \\ \\ \\ \\ \bar{x} = 5.4 \\ \\ \mu = 5 \\ \\ s = 2.408319 \\ \\ n = 5 \\ \\ \alpha = 0.05 \\ \\ H_{0}: \mu = 5 \\ \\ H_{a}: \mu > 5 \\ \\ df=n-1= 5 -1 \\ \\ \Rightarrow 4 \\ \\ critical\;value\;t\;=\;\;\mathbf{\color{Red}{2.131847}} \\\;\\\;Formula\;for\;test\;statistic\;t\;is \\ \\ t= \frac{\bar{x} - \mu }{\frac{s }{\sqrt{n}}} \\ \\ \\ So, t = \frac{5.4-5}{\frac{2.408319}{\sqrt{5}}} \\ \\ \Rightarrow \frac{0.4}{1.077033} \\ \\ \Rightarrow 0.371391 \\ \\ test\;statistic\;= \mathbf{\color{Red}{0.371391}} \\ \\ p= 0.364591 \\ \\ p\;is\;more\;than\;\alpha\;.\; So,\;Failed\;to\;Reject\;H_{0} } $$
$$ \displaylines{} $$
$$ \displaylines{} $$