Questions: (a) Find the P - value for the test statistic z=-1.41 for the following null and alternative hypotheses: H0: The population mean is 50. Ha: The population mean is less than 50. The P - value is

Solution Steps

We are testing the following hypotheses:

• Null Hypothesis $H_0$: The population mean is $\mu = 50$.
• Alternative Hypothesis $H_a$: The population mean is less than $50$.

For the given test statistic $z = -1.41$, we define the Z-score range for the left-tailed test:

• Lower bound: $-\infty$
• Upper bound: $-1.41$

The P-value is calculated as follows: $$P = \Phi(Z_{end}) - \Phi(Z_{start}) = \Phi(-1.41) - \Phi(-\infty)$$ From the calculations, we find: $$P = 0.0793$$

Final Answer