**Title: Understanding Hypothesis Testing in Survey Analysis****Introduction:**An annual survey of first-year college students asks 270,000 students about their attitudes on various subjects. According to a recent survey, 52% of first-year students believe that abortion should be legal. We aim to test the claim that over half of all first-year students believe that abortion should be legal using a 0.05 significance level.---**Objective:**Formulate the null and alternative hypotheses. Choose the correct answer from the options below.**Options:**- **A.** \( H_0: p = 0.5 \) \( H_a: p \neq 0.5 \)- **B.** \( H_0: p = 0.5 \) \( H_a: p > 0.5 \)- **C.** \( H_0: p = 0.5 \) \( H_a: p < 0.5 \)- **D.** \( H_0: p < 0.5 \) \( H_a: p = 0.5 \)**Explanation:**In hypothesis testing, the null hypothesis (\( H_0 \)) is a statement that there is no effect or no difference. It is the hypothesis that the researcher tries to disprove. The alternative hypothesis (\( H_a \)) is what the researcher wants to prove. Here, the goal is to test whether over half (\( p > 0.5 \)) of the population believes that abortion should be legal.**Tip for Choosing the Correct Hypothesis:**- **Null Hypothesis (\( H_0 \)):** Suggest no change or effect, typically \( p = 0.5 \).- **Alternative Hypothesis (\( H_a \)):** Suggests the effect or difference you want to test, e.g., \( p > 0.5 \).The correct choice aligns with testing whether more than half believe abortion should be legal, which is option **B.**By exploring hypothesis testing in this context, students can better understand statistical methods and their practical applications.

first of all we have to construct null and alternative hypotheses as follows we know that null hypothesis always contain sign ≤, ≥,= and alternative hypothesis always contain sign <,>,≠ Null and alternative hypothesis can be stated as follows :- H0: p =0.5 H1:p>0.5 (claim ) option B is correct. (test is right-tailed) It means rejection region will be right side, we know that area of rejection region must be equal to level of significance. From normal table we have P( Z<1.645 ) = 0.05 hence critical value is 1.645 Next step is to find test statistic, formula for test statistics z=(p^−p)/√(pq) /n Where p^=0.52 ( given ) n is total sample size taken = 270000 Calculation:- Z= (0.52- 0.5)/√(0.5*0.5/270000) = 0.02 /√(0.5*0.5/270000) = 20.7846 RULE:- if absolute value of test statistic is greater than absolute value of critical value then we have to reject null hypothesis. Hence we reject null hypothesis.in Other words we can say that there is sufficient evidence to conclude that result is significant.or we can conclude that there is sufficient evidence to support alternative hypothesis. Hence claim is correct