Consider a basketball player who makes 90% of free throws throughout the season. In a particular game, this basketball player attempted 15 free throws. Let X equal the number of free throws made by the basketball player during the game.
Do you think that the 15 free throw attempts are independent observations?
Yes, the 15 free throw attempts are likely to be independent observations. The independence assumption holds if the outcome of one event (attempting a free throw) does not affect the outcome of the next event. In this case, the success or failure of each free throw does not depend on the previous attempts or outcomes.
Yes, the 15 free throw attempts can be assumed to be independent observations. This means that the outcome of one free throw attempt does not affect the outcome of another free throw attempt. In other words, the success or failure of a previous free throw does not impact the likelihood of success or failure of the next free throw.
To determine whether the 15 free throw attempts are independent observations, we need to consider the definition of independence.
In statistics, two events or observations are considered independent if the outcome of one event does not affect the outcome of the other event. In this case, each free throw attempt is an event, and we want to determine if the outcomes (making or missing a free throw) of one attempt affect the outcomes of subsequent attempts.
In general, free throw attempts in a basketball game can be dependent on each other. Factors such as fatigue, confidence, and pressure can influence a player's performance. However, based on the given information, we cannot definitively conclude whether the 15 free throw attempts are independent or dependent.
To further analyze this situation, we would need additional data and context about the game, such as the time elapsed between free throws, the player's mental and physical condition during the game, and any factors that may influence their performance.