Question

Assume that we want to construct a confidence interval. Do one of the​ following, as​ appropriate: (a) find the critical value t Subscript alpha divided by 2​, ​(b) find the critical value z Subscript alpha divided by 2​, or​ (c) state that neither the normal distribution nor the t distribution applies.
The confidence level is 95​%, sigma is not​ known, and the histogram of 60 player salaries​ (in thousands of​ dollars) of football players on a team is as shown.

Answer 1

Answer:

Neither the normal distribution nor the t distribution applies.

Step-by-step explanation:

Hello!

The histogram attached shows the salary (in dollars) of 63 football players.

As you can see most of the values of this distribution are around 0 and the distribution is extremely asymmetrical (right skewed).

To apply a t-test to study the population average the population has to have a normal distribution.

The same goes for the standard normal distribution, but in this case, considering that the sample is large enough (n≥30) you can apply the Central Limit Theorem and approximate the distribution of the sample mean to normal X[bar]≈N(μ;δ²/n), but since the population variance is unknown, this is also not applicable.

The correct choice is the last one, since the conditions to apply the t test and the standard normal are not met.

I hope this helps!