Question

Let X be the number of goal chances that result in goals for a football team over n goals chances. During many matches, the team gets goals of 20% of the chances.

a) Explain why it might be reasonable (at least as an approach) to assume that X is binomially distributed in this situation. Do this by going through each of the points that must be met in order for us to use binomial distribution, assess whether it is reasonable that they are met here, and specify any additional assumptions we need to make. solved

Not solved:

What is the probability that the team gets two goals in a match with n = 12 goal chances?
What is the probability that they will get more than 50 targets in a season if they get n = 300 target chances?

Before a new season acquires two new spikes in hopes of increasing the likelihood of scoring on the target chances. During the first 116 goals they received 29 goals.
b) Determine with a hypothesis test whether the probability of scoring on the target chances has increased. Use 5% level. Also calculate the p-value of the test.
What would have been the conclusion of the test if we had used a 10% level?

Answer 1

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