In recent years, professional sports have incorporated the use of instant replay

Question

In recent years, professional sports have incorporated the use of instant replay in order to dispute questionable calls by the referees. For example, in the National football League a (NFL) a head coach is allowed to challenge the referees ‘decision twice per game. In order for the referees to reverse their original decision, the instant replay must exhibit clear evidence to the contrary.

Suppose the referees rule that, a pass was caught in bounds. The head coach of the opposing team believes the player stepped out of bounds before completely catching the ball and the coach challenges the referees’ decision.

The referees will review all available evidence (video taken from different camera angles) and make a decision. If there is evidence beyond a reasonable doubt that their original call was incorrect, the play will be called an incomplete pass, However, if there is no clear evidence to contradict the original call, the play will remain ruled as a compete pass

Notice the similarity between the decision to change a call and the decision to reject the null hypothesis in a hypothesis test. The process involves collecting convincing evidence that the original call or the null hypothesis is not true the referee only rejects the call if the instant replay exhibits clear evidence to the contrary. In both cases, not changing the call and not rejecting the null hypothesis doesn’t mean that the original call or the null hypothesis was correct; it means that not enough evidence was provided to the contrary.

To formulate the process as a hypothesis test, the null hypothesis is that the player _________, and the alternative hypothesis is that the player _________. The testing procedure then assumes that the player________, with a goal of determining whether there is enough evidence to infer that the player.

After the referees review video of all possible, camera angles, according to the process of a hypothesis test, what two possible decisions can the referees make? Check all that apply. (Hint: Remember that there are two possible decisions from a hypothesis test: you can either reject the null hypothesis or fail to reject the null hypothesis. Rejecting the null hypothesis means, you have convincing evidence that the null hypothesis is false and the alternative hypothesis is true Failing to reject the null means you do not have convincing evidence that the null hypothesis is false

___ Conclude that they do not have convincing evidence to support the hypothesis that the player caught the ball out of bounds.

___Conclude that they do not have convincing evidence to support the hypothesis that the player caught the ball in bounds

___ Conclude that they have convincing evidence to support the hypothesis that the player caught the ball in bounds

___ Conclude that the player caught the ball in bounds

___ Conclude that they have convincing evidence to support the hypothesis that the player caught the ball out of bounds

A Type II error occurs when you __________ a ________ null hypothesis. In this case, A Type I error corresponds t the referees concluding that they _________ evidence to support the hypothesis that the player _______when the payer actually___________.

A Type II occurs when you ______a ______ null hypothesis. In this case, a Type II error corresponds to the referees concluding that they ________evidence to support the hypothesis that the player ________ when the player actually_____________.

Explanation / Answer

We want to test the head coach's claim that the player stepped out of bounds before completely catching the ball.

Therefore,

The null hypothesis is ' The player CAUGHT THE BALL IN BOUNDS.'

Against alternative hypothesis ' The player CAUGHT THE BALL OUT OF BOUNDS.'

The testing procedure then assumes that the player CAUGHT THE BALL IN BOUNDS , with a goal of determining whether there is enough evidence to infer that the player CAUGHT IT OUT OF BOUNDS.

Since, conclusion is always made regarding the null hypothesis (i.e. player caught the ball in bounds), the possible decisions that the referees can make are

1) there is enough evidence to support the null hypothesis( ball was caught in bounds)

2) there is not enough evidence to support the null hypothesis

Accordingly, We choose the 2nd, 3rd and 4th Option.

Now, a type I error occurs if we reject the null hypothesis when it is true. Therefore, type I error occurs when you REJECT a TRUE null hypothesis. In this case, type 1 error corresponds to the decision that 'They DO NOT HAVE convincing evidence to support the hypothesis(null) that the player CAUGHT THE BALL IN BOUNDS, when the player actually CAUGHT THE BALL IN BOUNDS.'

A type II error occurs when we accept the null hypothesis when it is not true. Therefore, we say, type II error occurs when you ACCEPT a FALSE null hypothesis. Here, it corresponds to the referees concluding that 'They HAVE convincing evidence to support the hypothesis that the player CAUGHT THE BALL IN BOUNDS, when the player actually CAUGHT THE BALL OUT OF BOUNDS.'

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