Careers in science: A survey asked 590 people whether they had ever considered a career in science, and 320 said that they had. Can you conclude that the percentage of people who have considered a career in science is more than \( 50 \% \) ? Use the \( \alpha=0.05 \) level of significance. \( H_{0}: p=0.5 \) Part: \( 0 / 3>0.5 \) Part 1 of 3 (a) Find the \( P \)-value. Round your answer to at least four decimal places. The \( P \)-value is 0.0197 , Part: \( 1 / 3 \) Part 2 of 3 (b) What is the decision? Reject \( H_{0} \) Do not reject \( H_{0} \)

To determine whether we reject or fail to reject the null hypothesis, we need to consider both the \( P \)-value and the significance level \( \alpha \). Since the \( P \)-value of 0.0197 is less than \( \alpha = 0.05 \), we have enough evidence to reject the null hypothesis (\( H_0: p = 0.5 \)). This indicates that there is significant evidence to conclude that more than 50% of the surveyed people have considered a career in science! Now, the conclusion here isn’t just about numbers. This decision helps steer educational institutions and career programs to emphasize science-related fields, encouraging more students to explore fascinating careers in science! Researching the historical trends of STEM career interest shows that various factors impact whether individuals consider a career in science. This might include media influences, school programs, or notable scientists in the public eye. Looking into shifts in public interest through the years can provide rich insights into how society perceives science careers and might even spark ideas for improving outreach and education strategies!