Finding a P-Value In Exercises 13–18, find the P-value for the hypothesis test with the standardized test statistic z. Decide whether to reject H0 for the level of significance alpha.
Left-tailed test


z=-1.68
alpha=0.05

Verified step by step guidance

1. Step 1: Understand the problem. This is a left-tailed hypothesis test where the standardized test statistic z = -1.68, and the level of significance (α) is 0.05. The goal is to find the P-value and decide whether to reject the null hypothesis (H₀).
2. Step 2: Recall that the P-value in a left-tailed test is the area under the standard normal curve to the left of the given z-score. Use a standard normal distribution table or a statistical software to find the cumulative probability corresponding to z = -1.68.
3. Step 3: Compare the P-value obtained in Step 2 with the level of significance α = 0.05. If the P-value is less than or equal to α, reject the null hypothesis (H₀). Otherwise, fail to reject H₀.
4. Step 4: Interpret the result. If you reject H₀, it means there is sufficient evidence to support the alternative hypothesis (H₁) at the given level of significance. If you fail to reject H₀, it means there is insufficient evidence to support H₁.
5. Step 5: Summarize the findings in the context of the problem, ensuring clarity about whether the null hypothesis was rejected or not based on the comparison of the P-value and α.

Key Concepts

P-Value

The P-value is a statistical measure that helps determine the significance of results in hypothesis testing. It represents the probability of obtaining a test statistic at least as extreme as the one observed, assuming the null hypothesis is true. A smaller P-value indicates stronger evidence against the null hypothesis.

Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions about a population based on sample data. It involves formulating a null hypothesis (H0) and an alternative hypothesis (H1), then using sample data to determine whether to reject H0. The outcome is often influenced by the chosen significance level (alpha).

Significance Level (Alpha)

The significance level, denoted as alpha (α), is the threshold for deciding whether to reject the null hypothesis. Commonly set at 0.05, it represents a 5% risk of concluding that a difference exists when there is none. If the P-value is less than alpha, the null hypothesis is rejected, indicating statistically significant results.