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. Give alternative hypotheses

4. Determine the sampling distribution of ˆp if the null hypothesis is true

5. State a conclusion within the context of the problem.

Answer 1

Solution :

This is the less tailed test .

The null and alternative hypothesis is

H₀ : p = 0.60

H_a : p < 0.60

= x / n = 180 / 200 = 0.54

P₀ = 0.60

1 - P₀ = 0.40

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

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

= -1.73

P(z < -1.73) = 0.0418

P-value = 0.0418

= 0.05

P-value <

Reject the null hypothesis .

There is sufficient evidence that your friend’s “true proportion” of putts made from ten feet away is actually less than 60% .