In a campus-wide survey, 23 out of 282 respondents said that they approve of the way the president is handling the job.

Construct a 94% confidence interval for the true proportion of the students that approve the way the president is handling the job.

  1. Procedure:
  2. Assumptions: (select everything that applies)
  3. Unknown parameter:  
  4. Point estimate: = (Round the answer to 3 decimal places)
  5. Confidence level % and α=\displaystyle \alpha= , also
    •  α2=\displaystyle \frac{\alpha}{{2}}= , and 1α2=\displaystyle {1}-\frac{\alpha}{{2}}=
    • Critical values: (Round the answer to 3 decimal places)
      • left= right=
  6. Margin of error (if applicable): (Round the answer to 3 decimal places)
  7. Lower bound: (Round the answer to 3 decimal places)
  8. Upper bound: (Round the answer to 3 decimal places)
  9. Confidence interval:(, )
  10. Interpretation: We are % confident that the true population proportion is between % and %.
Based on the confidence interval, is it reasonable to believe that the population proportion is less than 9%? Explain.
, because 9%.