Question

Determine the sufficient evidence to reject the null hypothesis in favor of alternative hypothesis.

Right-tailed test

$\left(a\right)z=2.03\left(b\right)z=-0.31$

Short answer

(a) The P-value is$0.021178$.

(b) The P-value is$0.62712$.

Step-by-step solution

Step 1. Given

Right-tailed test

$\left(a\right)z=2.03\left(b\right)z=-0.31$

Part(a) Step 2. Calculation

Since the given hypothesis test is a Right-tailed test, the P-value is given by

$$\begin{gathered} P-\mathrm{value}=P(z\ge z_0),\mathrm{where}z~N(0,1) \\ =P(z\ge 2.03) \\ =1-P(z<2.03) \\ =1-0.978822 \\ =0.021178 \end{gathered}$$

Part(b) Step 3. Calculation

Since the given hypothesis test is a Right-tailed test, the P-value is given by

$$\begin{gathered} P-\mathrm{value}=P(z\ge z_0),\mathrm{where}z~N(0,1) \\ =P(z\ge -0.31) \\ =1-P(z<-0.31) \\ =1-0.37828 \\ =0.62172 \end{gathered}$$