Question

Rex wanted to estimate the mean finishing time for the approximately 50 , 000 50,00050, comma, 000 finishers at the New York City Marathon. He took a random sample of 10 1010 finishers' times, which were skewed to the right with a sample mean of x ˉ = 271. 5 x ˉ =271. 5x, with, \bar, on top, equals, 271, point, 5 minutes. He's considering using his data to make a confidence interval for the mean finishing time. Which conditions for constructing a t tt interval have been met? Choose all answers that apply: Choose all answers that apply: (Choice A) A The data is a random sample from the population of interest. (Choice B) B The sampling distribution of x ˉ x ˉ x, with, \bar, on top is approximately normal. (Choice C) C Individual observations can be considered independent

Answer 1

The data is a random sample from the population of interest.

Individual observations can be considered independent.

Explanation:

From Khan Academy

The random condition:

The problem reads, "He took a random sample of 10 finishers' times," so the random condition is met.

The normal condition:

The times in the sample were skewed, and the sample size is small (n=10<30)(n=10<30)left parenthesis, n, equals, 10, is less than, 30, right parenthesis, so the normal condition has not been met.

The independence condition:

The independence condition says that when sampling without replacement, we can still treat each observation in the sample as independent as long as we sample less than 10%, percent of the population. Since the sample of 10 finishers' times is less than 10%, percent of the approximately 50,000 times in the population, the independence condition has been met.

The answers:

The data is a random sample from the population of interest.

Individual observations can be considered independent.