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 99% confidence and obtained the values: 57 and 79.

a)Interpret these values in the context of the problem.

• We can be 99% confident that the population mean score is between 57 and 79.
• There is a 99% chance that the sample mean score is between 57 and 79.
• There is a 99% chance that the population mean score is between 57 and 79.
• The likelihood of obtaining a sample mean between 57 and 79 is approximately 99%

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 92% confidence, what (if anything) can be said about this confidence interval?

• The 92% confidence interval would be wider
• The 92% confidence interval would be more narrow.
• It is impossible to tel