Question

Jacob usually scored 65% of his shots. He has played for a while and is playing today. We test the hypothesis that his chance of scoring is still as good as before, at 66%. 1. Write the null and alternative hypotheses ??0 and ??1 2. What would the Type I error be? 3. What would the Type II error be? 4. If the data suggests that we should reject the null hypothesis, write the verbal conclusion in context.

Answer 1

Solution

Back-Up Theory

Type I Error is the error of rejecting a null hypothesis when it is true. ...........................................................(1)

Type II Error is the error of accepting a null hypothesis when it is not true, i.e., Alternative is true. ............. (2)

Now To Work Out The Solution,

Let p represent the chance (probability) of scoring.

Part (1)

Hypotheses:

Null H₀ : p = p₀ = 0.66 [i.e., 66%] [in real terms: chance of scoring is still as good as before]

Vs

Alternative: H₁ : p < 0.66 [in real terms: chance of scoring is lower than before]

Answer 1

Part (2)

Vide (1), contextually, Type I error is declaring that the chance of scoring is lower than before, when actually, chances are as good as before. Answer 2

Part (3)

Vide (2), in the present scenario, Type II error is declaring that the chances are as good as before when actually, chance of scoring is lower than before,. Answer 3

Part (4)

Rejecting the null hypothesis in this context would mean that chance of scoring is lower than before,. Answer 4

DONE