A recent survey by the research institute showed that62%of users of online dating sites say the number one thing they're looking for in a date or partner is common interests. Suppose you would like to perform a hypothesis test to challenge this finding. From a random sample of130students on campus, you find that70said the number one thing they're looking for in a date or partner is common interests. Using a =0.05,complete parts a and b. **Educational Text for Hypothesis Testing**---**Context:**A recent survey conducted by a research institute found that 62% of users of online dating sites state that the primary characteristic they seek in a date or partner is having common interests. Suppose you conduct a hypothesis test to verify this finding. In a random sample of 130 students on campus, 70 students reported that common interests are what they primarily look for in a date or partner. Using a significance level of α = 0.05, analyze parts a and b.**Task a:**Based on this sample, we need to determine whether the proportion of students who said the number one thing they're looking for in a date or partner is common interests is similar to the research institute's survey findings.**Determine the Null and Alternative Hypotheses:**Choose the correct formulation:- **A.** \( H_0: p \geq 0.62 \) \( H_1: p > 0.62 \)- **B.** \( H_0: p = 0.62 \) \( H_1: p \neq 0.62 \)- **C.** \( H_0: p > 0.62 \) \( H_1: p \le 0.62 \)- **D.** \( H_0: p \ge 0.62 \) \( H_1: p < 0.62 \)**Explanation:**The objective is to test whether the sample proportion differs significantly from 0.62 as per the original survey findings. The null hypothesis (\(H_0\)) represents the assumption that any deviation from the original survey result is due to random chance, while the alternative hypothesis (\(H_1\)) considers the possibility of a significant difference. Select the option that correctly sets up these hypotheses for the hypothesis test at the 5% significance level.---By analyzing these hypotheses, students can engage in understanding and applying statistical principles to real-world data, honing their skills on formulating and testing hypothesis in statistics.

Solution-: Given: We find (a) Determine null and alternative hypothesis (b) Test the given claimHere, we use proportion test (Z-test) (a) Hypothesis: Vs (Two tailed test) Option (B) ; is correct(b) Test the given claim The test statistic is given by, Table value or Critical value: (From Z-table) Decision Rule: If we reject or otherwise fail to reject Here, Hence, we fail to reject at 5% level of significance. Conclusion:- We conclude that, common interest is similar to the research institute survey.