a. Test the claim using a hypothesis test Consider the first sample to be the sample of males and the second sample to be the sample of females. What are the null and alternative hypotheses for the hypothesis test? O A. Ho P1 SP2 H: P1 P2 OB. Ho Pi P2 H P =P2 OC. Ho P1 P2 H P P2 O D. Ho P12 P2 H Pi+P2 VE. Ho P1 P2 H Pi

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### Hypothesis Testing Example: Left-Handedness in Males vs. Females

**Scenario:**
In a random sample of males, 24 out of 246 individuals write with their left hands. In a random sample of females, 68 out of 525 individuals write with their left hands. We use a 0.01 significance level to test the hypothesis that the rate of left-handedness among males is less than that among females.

**Task:**
Test the claim using a hypothesis test.

**Steps:**

1. **Define Samples:**
   - **First Sample:** Males
   - **Second Sample:** Females

2. **Formulate Hypotheses:**
   - **Null Hypothesis (H₀):** \( p_1 = p_2 \) (The proportion of left-handed males is equal to the proportion of left-handed females.)
   - **Alternative Hypothesis (H₁):** \( p_1 < p_2 \) (The proportion of left-handed males is less than the proportion of left-handed females.)

3. **Identify the Test Statistic:**
   - z = -1.28 (rounded to two decimal places)

4. **Identify the P-value:**
   - The P-value is not provided and should be calculated based on the z statistic.

### Graphs and Diagrams
This image contains no graphs or diagrams that require further explanation. The focus is on the hypothesis test setup, including defining hypotheses and calculating the test statistic.
Transcribed Image Text:### Hypothesis Testing Example: Left-Handedness in Males vs. Females **Scenario:** In a random sample of males, 24 out of 246 individuals write with their left hands. In a random sample of females, 68 out of 525 individuals write with their left hands. We use a 0.01 significance level to test the hypothesis that the rate of left-handedness among males is less than that among females. **Task:** Test the claim using a hypothesis test. **Steps:** 1. **Define Samples:** - **First Sample:** Males - **Second Sample:** Females 2. **Formulate Hypotheses:** - **Null Hypothesis (H₀):** \( p_1 = p_2 \) (The proportion of left-handed males is equal to the proportion of left-handed females.) - **Alternative Hypothesis (H₁):** \( p_1 < p_2 \) (The proportion of left-handed males is less than the proportion of left-handed females.) 3. **Identify the Test Statistic:** - z = -1.28 (rounded to two decimal places) 4. **Identify the P-value:** - The P-value is not provided and should be calculated based on the z statistic. ### Graphs and Diagrams This image contains no graphs or diagrams that require further explanation. The focus is on the hypothesis test setup, including defining hypotheses and calculating the test statistic.
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