Final answer:
The P-value for each z-test statistic is determined using the standard normal distribution. Values with P-value less than α = 0.05 indicate that the null hypothesis should be rejected. Decisions are based on the comparison between P-value and α.
Step-by-step explanation:
The question is asking to find the P-value associated with given z-test statistic values for a large-sample z test where the null hypothesis H0: μ = 5 and the alternative hypothesis Ha: μ > 5. To find the p-value for each z-test statistic, we look to the right tail of the standard normal distribution. The larger the z-score, the smaller the P-value, which means the evidence against the null hypothesis is stronger.
- For z = 1.42, the P-value is approximately 0.0778 (from z-tables).
- For z = 0.90, the P-value is approximately 0.1841.
- For z = 1.96, the P-value is approximately 0.0250.
- For z = 2.48, the P-value is approximately 0.0066.
- For z = 2.11, the P-value is approximately 0.0174.
Comparing each P-value with the significance level α = 0.05, we can make a decision regarding the null hypothesis. If P-value < α, we reject H0; otherwise, we do not reject H0.
Here are the decisions based on the given z-scores:
- a. For z = 1.42, since P-value > α, do not reject H0.
- b. For z = 0.90, since P-value > α, do not reject H0.
- c. For z = 1.96, since P-value is approximately equal to α, we might reject H0 depending on the exact critical value used.
- d. For z = 2.48, since P-value < α, reject H0.
- e. For z = 2.11, since P-value < α, reject H0.