Learning to ski as an adult can be a daunting task. Many ski resorts offer skiing lessons for adults with the hope of increasing attendance. Ski University would like to advertise their quality ski instructors by estimating the population mean number of lesson hours it takes for adult learn-to-ski participants to “graduate” from their program, that is, to ski comfortably on their own. A random sample of 27 recent adult learn-to-ski participants at Ski University was obtained, and each was asked to report the amount of lesson hours they took to graduate. As a result of the study, a 98% confidence interval was found to go from 2.4 lesson hours to 4.6 lesson hours.

Part 1: Provide an estimate of the population mean number of lesson hours it takes to graduate for all recent adult learn-to-ski participants at Ski University.

Part 2: Complete statement: “We estimate, the average distance of the possible _______________ (for repeated samples of the same size n) from the ___________ to be about ______ lesson hours.”

Part 3: Complete statement: “We estimate, the average distance of the possible _______________ from the ___________ to be about ______ lesson hours.”

Part 4: We need to determine if all assumptions are met. The first assumption of having a random sample of recent Ski University adult learn-to-ski participants is met. Is the following statement about the second assumption correct or incorrect?

The second assumption that is required is that we need to assume that the population mean number of lesson hours it takes recent Ski University adult learn-to ski-participants to graduate has a normal distribution.

Part 5: Is the following statement about the resulting confidence interval correct or incorrect?

“We are 100% confident that the sample mean number of lesson hours it takes recent Ski University adult learn-to-ski participants to graduate is between 2.4 lesson hours and 4.6 lesson hours.”

Part 6: Is the following statement about the meaning of the 98% confidence level correct or incorrect?

“The probability that the population mean number of lesson hours it takes recent Ski University adult learn-to-ski participants to graduate is between 2.4 lesson hours and 4.6 lesson hours is 0.98.”

Part 7: Is the following statement about the interpretation of the confidence interval correct or incorrect?

“We estimate, with 98% confidence, that the population mean number of lesson hours it takes recent Ski University adult learn-to-ski participants to graduate to be somewhere between 2.4 lesson hours and 4.6 lesson hours.”

(Would really appreciate explanations in context and steps to help me understand! Thank you!)