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