A local athletic facility offers a four-week training course, hoping to increase athletes’ running speeds. Thirty-five volunteer athletes are timed, in seconds, running a 50-yard dash before the training program begins and then again after the program is complete. The difference in running times (before training – after training) is calculated for each athlete. Are the conditions for inference met?

No. The athletes who volunteered for this study were not randomly assigned a treatment order.
No. The 10% condition is not met.
No. The Normal/Large Sample condition is not met because the sample size is too small.
Yes. All conditions are met.

It states that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the sampling distribution is also approximately normal, as long as n is at least 30.

In this problem, we have no information about the distribution, but the sample size is greater than 30, hence all the conditions have been met.

More can be learned about the Central Limit Theorem at https://brainly.com/question/24663213

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