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= 1.95
alpha=0.08

Verified step by step guidance

1. Step 1: Understand the problem. This is a left-tailed hypothesis test where the standardized test statistic z = 1.95, and the level of significance (α) is 0.08. 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 to the left of the given z-score on the standard normal distribution curve. Use a z-table, statistical software, or a calculator to find the cumulative probability corresponding to z = 1.95.
3. Step 3: Compare the P-value obtained in Step 2 to the level of significance α = 0.08. 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 the null hypothesis is rejected, it means there is sufficient evidence to support the alternative hypothesis at the given level of significance. If the null hypothesis is not rejected, it means there is insufficient evidence to support the alternative hypothesis.
5. Step 5: Summarize the decision. Clearly state whether H₀ is rejected or not based on the comparison between 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 (H0) is true. A smaller P-value indicates stronger evidence against H0, leading to a potential rejection of 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 two competing hypotheses: the null hypothesis (H0), which represents no effect or no difference, and the alternative hypothesis (H1), which represents the effect or difference. The outcome of the test helps determine whether to reject H0 in favor of H1.

Level of Significance (Alpha)

The level of significance, denoted as alpha (α), is the threshold for deciding whether to reject the null hypothesis. It represents the probability of making a Type I error, which occurs when H0 is incorrectly rejected. Common alpha levels are 0.05 and 0.01, but in this case, it is set at 0.08, meaning there is an 8% risk of rejecting H0 when it is actually true.