2022 spring-final exam paper-on X Juvi Online Survey Software | Qualtric X HoBan BKnaka X + extension://oemmndcbudboiebfnladdacdfmadadm/https://brightspace.nyu.edu/d21/common/viewFile.d2|file/Database + ABTOMATNyeCKN 2. The costs associated with conducting interviews for a job opening have skyrocketed over the years. According to a survey, we find that 230 out of 400 senior human resources executives believe that their hiring managers are interviewing too many people to find qualified candidates. (a) Please find a 95% confidence interval for the proportion of senior human resources executives who believe that their hiring managers interview too many candidates during a job search. (10 pts) (b) If we hope the width of the confidence interval in part a is equal to 0.1, how many senior human resources executives should be sampled? (5 pts) (c) Is it reasonable that the proportion of senior human resources executives who believe their hiring managers interview too many candidates is greater than 50%? Please test with 0.05 level of significance. (10 pts) 3. Educators are constantly evaluating the efficacy of public schools in the education. To check how average math SAT scores changes over time, we randomly selected 7 states and recorded the math SAT scores for the years 2014 and 2010 for each of the 7 states, which are shown as below. Please test whether the true mean math SAT score in 2014 differs from the true mean in 2010. Use 0.05 level of significance. (10 m to ) EN B P3 21'C Light rain acer W