Question

You are tracking Chipotle Mexican Grill's stock price, attempting to figure out a good price point for entry into the market. You look at 37 random days over the course of a few months and see that the closing price has an average of $263.43 with a standard deviation of $20.451. You construct a 99% confidence interval for the average stock price to be (254.29, 272.57). Of the following choices, what is the appropriate interpretation of this interval?

Question 4 options:

1)	We are certain that 99% of the daily closing prices will be between $254.29 and $272.57.

2)	We cannot determine the proper interpretation of this interval.

3)	We are 99% confident that the proportion of all days that have a closing price between $254.29 and $272.57 is 99%

4)	We are 99% confident the average daily closing price for any day is between $254.29 and $272.57

5)	We are 99% confident the average daily closing price for the days monitored is between $254.29 and $272.57.

Answer 1

Please don't hesitate to give a "thumbs up" in case you're satisfied with the answer

n = 37

Mean = 263.43

Stdev = 20.451

99% CI is (254.29, 272.57)

We are 99% Confident that the average daily closing price for any days is between $254.29 to $272.57

4. is therefore the correct interpretation because:

The 99% is not about the proportion, it is for all days ( so any is correct, only days monitored ) is wrong.

Hence, 5, 3 are wrong. Confidence interval doesn't tell certainty, so 1) is ruled out. 4) is the correct interpretation