One Tailed and Two Tailed Tests

One Tailed Test		Two Tailed Test
\(H_0 : \mu = \mu_0 ; H_1 : \mu > \mu_0\) Method I \(z_{\text{critical}} = \text{inVNorm}\hspace{0.1em}\left(\frac{\alpha}{100}, 0, 1, \text{right}\right)\) \(z_{\text{stat}} = \frac{\bar{x} - \mu_0}{\sqrt{\frac{\sigma^2}{n}}}\) or \(\frac{\bar{x} - \mu_0}{\sqrt{\frac{s^2}{n}}}\) Reject \(H_0\) when \(z_{\text{stat}} \ge z_{\text{critical}}\).	\(H_0 : \mu = \mu_0 ; H_1 : \mu < \mu_0\) Method I \(z_{\text{critical}} = \text{inVNorm}\hspace{0.1em}\left(\frac{\alpha}{100}, 0, 1, \text{left}\right)\) \(z_{\text{stat}} = \frac{\bar{x} - \mu_0}{\sqrt{\frac{\sigma^2}{n}}}\) or \(\frac{\bar{x} - \mu_0}{\sqrt{\frac{s^2}{n}}}\) Reject \(H_0\) when \(z_{\text{stat}} \le z_{\text{critical}}\).	\(H_0 : \mu = \mu_0 ; H_1 : \mu \neq \mu_0\) Method I \(z_{\text{critical}} = \text{inVNorm}\hspace{0.1em}\left(1 - \frac{\alpha}{100}, 0, 1, \text{centre}\right)\) \(z_{\text{stat}} = \frac{\bar{x} - \mu_0}{\sqrt{\frac{\sigma^2}{n}}}\) or \(\frac{\bar{x} - \mu_0}{\sqrt{\frac{s^2}{n}}}\) Reject \(H_0\) when \(z_{\text{stat}} \le -z_{\text{critical}}\) or \(z_{\text{stat}} \ge z_{\text{critical}}\).
Method II: Reject \(H_0\) when \(p\)-value is less than significance level \(\alpha\%\)

One Tailed Test

Two Tailed Test

$H_0 : \mu = \mu_0 ; H_1 : \mu > \mu_0$

Method I

$z_{\text{critical}} = \text{inVNorm}\hspace{0.1em}\left(\frac{\alpha}{100}, 0, 1, \text{right}\right)$

$z_{\text{stat}} = \frac{\bar{x} - \mu_0}{\sqrt{\frac{\sigma^2}{n}}}$ or $\frac{\bar{x} - \mu_0}{\sqrt{\frac{s^2}{n}}}$

Reject $H_0$ when $z_{\text{stat}} \ge z_{\text{critical}}$.

$H_0 : \mu = \mu_0 ; H_1 : \mu < \mu_0$

Method I

$z_{\text{critical}} = \text{inVNorm}\hspace{0.1em}\left(\frac{\alpha}{100}, 0, 1, \text{left}\right)$

$z_{\text{stat}} = \frac{\bar{x} - \mu_0}{\sqrt{\frac{\sigma^2}{n}}}$ or $\frac{\bar{x} - \mu_0}{\sqrt{\frac{s^2}{n}}}$

Reject $H_0$ when $z_{\text{stat}} \le z_{\text{critical}}$.

$H_0 : \mu = \mu_0 ; H_1 : \mu \neq \mu_0$

Method I

$z_{\text{critical}} = \text{inVNorm}\hspace{0.1em}\left(1 - \frac{\alpha}{100}, 0, 1, \text{centre}\right)$

$z_{\text{stat}} = \frac{\bar{x} - \mu_0}{\sqrt{\frac{\sigma^2}{n}}}$ or $\frac{\bar{x} - \mu_0}{\sqrt{\frac{s^2}{n}}}$

Reject $H_0$ when $z_{\text{stat}} \le -z_{\text{critical}}$ or $z_{\text{stat}} \ge z_{\text{critical}}$.

Method II: Reject $H_0$ when $p$-value is less than significance level $\alpha\%$

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