Question

Suppose your golfing buddy states that they can make 60% of all putts they would ever hit from ten feet away from the hole. You think he is exaggerating, so you want to conduct a hypothesis test to see if there is evidence that your friend’s “true proportion” of putts made from ten feet away is actually less than 60%. You collect data by having him hit 200 putts and he makes 108 of them.

1. Describe the population.

2. Describe the sample.

3. Verify the condition

4. Give the null and alternative hypotheses

Answer 1

Solution :

Given that,

1)

P₀ = 60% = 0.60

1 - P₀ = 1 - 0.60 = 0.40

2)

n = 200

x = 108

= x / n = 108 / 200 = 0.54

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.54 - 0.60/ [(0.60 * 0.40) / 200]

z = -1.73

P(z < -1.73) = 0.0418

P-value = 0.0418

4)

This is the left tailed test .

The null and alternative hypothesis is ,

H₀ : p = 0.60

H_a : p < 0.60