Questions: Use the given information to find the P-value. Also, use a 0.05 significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis). With H1 : p>0.554, the test statistic is z=1.34. A. 0.0901; fail to reject the null hypothesis B. 0.0901; reject the null hypothesis C. 0.9099 ; fail to reject the null hypothesis D. 0.1802; reject the null hypothesis

Solution Steps

The Z-score is calculated using the formula:

\[ z = \frac{X - \mu}{\sigma} \]

Substituting the values:

\[ z = \frac{1.34 - 0}{1} = 1.34 \]

Thus, the Z-score is \( z = 1.34 \).

The P-value is determined using the cumulative distribution function \( \Phi \). For a right-tailed test, the P-value is calculated as:

\[ P = \Phi(Z_{end}) - \Phi(Z_{start}) = \Phi(\infty) - \Phi(1.34) \]

From the calculations, we find:

\[ P = 0.0901 \]

To make a decision regarding the null hypothesis, we compare the P-value to the significance level \( \alpha = 0.05 \).

Since \( P = 0.0901 > 0.05 \), we fail to reject the null hypothesis.

Final Answer