In a random sample of males, it was found that 22 write with their left hands and 220 do not. In a random sample of females, it was found that 70 write with their left hands and 452 don not. Use a 0.01 significance level to test the claim that the rate of left-handedness among males is less than that among females. Complete parts (a) through (c) below. z = -1.71 (Round to two decimal places as needed.) Identify the P-value. P-value= 0.044 (Round to three decimal places as needed.). What is the conclusion based on the hypothesis test? The P-value is greater than the significance level of a=0.01. so fail to reject the null hypothesis. There is not sufficient evidence to support the claim that the rate of left-handedness among males is less than that among females. b. Test the claim by constructing an appropriate confidence interval. The 98% confidence interval is < (P-P₂) < (Round to three decimal places as needed.)

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**Analysis of Left-handedness in Males and Females**

In a random sample of males, 22 out of 242 were found to write with their left hands. In a random sample of females, 70 out of 522 were left-handed. We want to test the claim that the rate of left-handedness among males is less than that among females using a 0.01 significance level. Below is the detailed analysis:

1. **Calculate the z-score:**

   \[
   z = -1.71
   \]

   *(Round to two decimal places as needed.)*

2. **Identify the P-value:**

   \[
   \text{P-value} = 0.044
   \]

   *(Round to three decimal places as needed.)*

3. **Conclusion Based on Hypothesis Test:**

   Since the P-value is greater than the significance level (\(\alpha = 0.01\)), we fail to reject the null hypothesis. There is not sufficient evidence to support the claim that the rate of left-handedness among males is less than that among females.

4. **Confidence Interval for the Difference in Proportions:**

   The 98% confidence interval for \( (p_1 - p_2) \) is:

   \[
   Solution: \, \text{Enter interval values here}
   \]

   *(Round to three decimal places as needed.)*

This analysis indicates no statistically significant difference in the rates of left-handedness between males and females at the 0.01 significance level.
Transcribed Image Text:**Analysis of Left-handedness in Males and Females** In a random sample of males, 22 out of 242 were found to write with their left hands. In a random sample of females, 70 out of 522 were left-handed. We want to test the claim that the rate of left-handedness among males is less than that among females using a 0.01 significance level. Below is the detailed analysis: 1. **Calculate the z-score:** \[ z = -1.71 \] *(Round to two decimal places as needed.)* 2. **Identify the P-value:** \[ \text{P-value} = 0.044 \] *(Round to three decimal places as needed.)* 3. **Conclusion Based on Hypothesis Test:** Since the P-value is greater than the significance level (\(\alpha = 0.01\)), we fail to reject the null hypothesis. There is not sufficient evidence to support the claim that the rate of left-handedness among males is less than that among females. 4. **Confidence Interval for the Difference in Proportions:** The 98% confidence interval for \( (p_1 - p_2) \) is: \[ Solution: \, \text{Enter interval values here} \] *(Round to three decimal places as needed.)* This analysis indicates no statistically significant difference in the rates of left-handedness between males and females at the 0.01 significance level.
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