(a) State the appropriate null and alternative hypotheses to assess whether women are taller today. (b) Suppose the P-value for this test is 0.16. Explain what this value represents. (c) Write a conclusion for this hypothesis test assuming an a = 0.05 level of significance.
(a) State the appropriate null and alternative hypotheses to assess whether women are taller today. (b) Suppose the P-value for this test is 0.16. Explain what this value represents. (c) Write a conclusion for this hypothesis test assuming an a = 0.05 level of significance.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:**Hypothesis Testing: Analyzing Women's Height Over Time**
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**Context:**
Several years ago, the average height of women aged 20 or older was recorded at 63.7 inches. A recent random sample of 45 women from this age group today shows a mean height of 64.8 inches.
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**Tasks:**
1. **State the Hypotheses:**
- Determine the null and alternative hypotheses to evaluate if women today are taller.
Options:
- A. H₀: μ = 64.8 in. vs. H₁: μ < 64.8 in.
- B. H₀: μ = 63.7 in. vs. H₁: μ < 63.7 in.
- C. H₀: μ = 63.7 in. vs. H₁: μ > 63.7 in.
- D. H₀: μ = 63.7 in. vs. H₁: μ ≠ 63.7 in.
- E. H₀: μ = 64.8 in. vs. H₁: μ > 64.8 in.
- F. H₀: μ = 64.8 in. vs. H₁: μ ≠ 64.8 in.
2. **Evaluate the P-value:**
- Provided P-value: 0.16
- Explain its significance: A P-value represents the probability of observing the results as extreme as those measured, assuming the null hypothesis is true.
3. **Draw a Conclusion (α = 0.05):**
- Consider whether the P-value is less than the significance level (α). If yes, reject the null hypothesis.
---
**Analysis:**
- **Appropriate Hypotheses Choice:** Option C is correct: H₀: μ = 63.7 in. vs. H₁: μ > 63.7 in.
- **P-value Interpretation:** A P-value of 0.16 suggests weak evidence against the null hypothesis. Since 0.16 > 0.05, we do not reject the null hypothesis.
- **Conclusion:** At a 0.05 significance level, there isn't enough statistical evidence to conclude women are taller today.
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