2 **Title: Analyzing Left-Handedness in Males and Females Using Hypothesis Testing and Confidence Intervals**In a study examining handedness, researchers found that out of a sample of 248 males, 26 were left-handed, while 222 were not. In a separate sample of 496 females, 58 were left-handed, and 438 were not. The goal is to test the hypothesis that the rate of left-handedness in males is less than that in females using a significance level of 0.01.**a. Hypothesis Test**We begin by defining our samples:- Sample 1: Males- Sample 2: FemalesThe null and alternative hypotheses are established as follows:- \( H_0: p_1 \ge p_2 \)- \( H_1: p_1 < p_2 \)**Identify the Test Statistic:**- Calculate the z-value for the test statistic.- Formula: \( z = \) (Guide students to compute, prompt for rounding to two decimal places.)**Identify the P-Value:**- Compute the P-value and round it to three decimal places.**Conclusion Based on Hypothesis Test:**- Depending on the P-value and significance level (\(\alpha = 0.01\)), we assess whether there is sufficient evidence to reject the null hypothesis in favor of the alternative. If \( \text{P-value} \leq \alpha \), reject \( H_0 \).**b. Confidence Interval Approach****Construct a 98% Confidence Interval:**- Use the difference in proportions: \( (p_1 - p_2) \)- Fill in the interval (prompt for rounding to three decimal places).**Conclusion Based on Confidence Interval:**- Examine whether the interval supports a significant difference, indicating if the male rate is indeed less.**c. Interpretation**We analyze the findings to recommend the appropriate conclusion:- **A.** Conclusion that no significant difference exists.- **B.** Evidence supports male rate lying below female rate.- **C.** Male rate not conclusively less than female rate.- **D.** Data validity questioned, tests not applicable.**Discussion:**- This educational exercise in statistical analysis helps draw conclusions about handedness tendencies, illustrating practical application of hypothesis testing and confidence intervals in real-world contexts.

Given data: Significance level = 0.01

In a random sample of males, it was found that 26 write with their left hands and 222 do not. In a random sample of females, it was found that 58 write with their left hands and 438 do 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. 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? OC. Ho: P1 =P2 O A. Hg: P1 =P2 H: P P2 O B. Ho: P = P2 H: P: