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Ch. 7 - Hypothesis Testing with One Sample
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoLarson 8th EditionCh. 7 - Hypothesis Testing with One SampleProblema 7.2.17
Capitolo 7, Problema 7.2.17

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

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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).
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.
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.
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.
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.

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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.
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Step 3: Get P-Value

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).
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Step 1: Write Hypotheses

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.
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Step 4: State Conclusion Example 4
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Ha: p = 0.25

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