Write out a proper interpretation for this confidence interval.

Question

The Professor from Gilligan's Island made a six sided die, each side numbered from 1 to 6, from a palm tree and wants to calculate a 90% confidence interval for what the true proportion would be when trying to roll a 1 with that die. He rolls the die 100 times and it comes up 1 24 times. Write out a proper interpretation for this confidence interval.

Answer 1

The Professor's 90% confidence interval for the true proportion of rolling a "1" with his homemade die is approximately 0.1700.170 to 0.3100.310. This means that we can be 90% confident that the true probability of rolling a "1" with this die lies between 17% and 31%.



It's important to note that this confidence interval does not imply that future rolls will fall within this range 90% of the time. Instead, it means that if we were to repeat this experiment many times, constructing a confidence interval in the same way each time, then approximately 90% of these confidence intervals would contain the true proportion of rolling a "1". ​