MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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**Example Question: Statistical Hypothesis Testing**

**Consider a hypothesis test about two proportions, H₀: p₁ = p₂ versus Hₐ: p₁ ≠ p₂. If the alternative hypothesis Hₐ is true, increasing the size of the two samples would tend to ________ the absolute value of the test statistic and ________ the p-value. The two blanks should be:**

(i) increase; increase

(ii) increase; decrease

(iii) decrease; increase

(iv) decrease; decrease

In hypothesis testing, when the sample size increases, the precision of the test improves. Assuming the alternative hypothesis \( H_a \) is true, typically we would expect:

1. **Absolute Value of Test Statistic**: As the sample size increases, the test statistic, which measures the degree of deviation from the null hypothesis, becomes more extreme (i.e., the absolute value increases).
2. **p-value**: The p-value, which indicates the probability of observing the test results under the null hypothesis, typically decreases with a larger sample size in the presence of a true effect.

Thus, the correct choice is (ii) **increase; decrease**.
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Transcribed Image Text:**Example Question: Statistical Hypothesis Testing** **Consider a hypothesis test about two proportions, H₀: p₁ = p₂ versus Hₐ: p₁ ≠ p₂. If the alternative hypothesis Hₐ is true, increasing the size of the two samples would tend to ________ the absolute value of the test statistic and ________ the p-value. The two blanks should be:** (i) increase; increase (ii) increase; decrease (iii) decrease; increase (iv) decrease; decrease In hypothesis testing, when the sample size increases, the precision of the test improves. Assuming the alternative hypothesis \( H_a \) is true, typically we would expect: 1. **Absolute Value of Test Statistic**: As the sample size increases, the test statistic, which measures the degree of deviation from the null hypothesis, becomes more extreme (i.e., the absolute value increases). 2. **p-value**: The p-value, which indicates the probability of observing the test results under the null hypothesis, typically decreases with a larger sample size in the presence of a true effect. Thus, the correct choice is (ii) **increase; decrease**.
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