Interpret a Confidence Interval: A center producing standardized exams for certifications wants to better understand its Six-Sigma certification exam. They were only able to access a small sample of their scores, so they used the confidence interval formula with 95% confidence and obtained the values: 58 and 82. a)Interpret these values in the context of the problem.

• The likelihood of obtaining a sample mean between 58 and 82 is approximately 95%
• We can be 95% confident that the population mean score is between 58 and 82.
• There is a 95% chance that the population mean score is between 58 and 82.
• There is a 95% chance that the sample mean score is between 58 and 82.

b) The point estimate can be recovered even if you only know the endpoints of the confidence interval. What was the average score of the exams in their sample? (round to one decimal place) c) If they were to calculate a new confidence interval at 96% confidence, what (if anything) can be said about this confidence interval?

• The 96% confidence interval would be more narrow.
• The 96% confidence interval would be wider
• It is impossible to tell