Question

Ten professional golfers are asked to hit each of two brands of golf ball with their drivers. The golfers do not know which brand they are hitting, and the order in which they hit the balls is determined by flipping a coin. Is there evidence that Brand 1 golf balls are hit a smaller distance, on average, than Brand 2 golf balls?

Golfer Brand 1 Brand 2

1 265 268

2 281 283

3 260 257

4 274 277

5 269 270

6 288 291

7 271 275

8 270 274

9 267 269

10 284 288

a. No since the p-value is greater than 0.05.

b. Yes at a 0.10 level of significance, but not at the 0.05 level.

c. Yes, since the p-value is less than 0.01.

d. Yes at the 0.05 level of significance, but not the 0.01 level.

Answer 1

Solution:

Here, we have to use paired t test.

The null and alternative hypotheses for this test are given as below:

Null hypothesis: H0: Brand 1 and Brand 2 golf balls are hit a same distance, on average.

Alternative hypothesis: Ha: Brand 1 golf balls are hit a smaller distance, on average, than Brand 2 golf balls.

H0: µd = 0 versus Ha: µd > 0

This is a right tailed test.

We consider difference as brand 2 minus brand 1.

Test statistic for paired t test is given as below:

t = (Dbar - µd)/[Sd/sqrt(n)]

From given data, we have

Dbar = 2.3

Sd = 2.1108

n = 10

df = n – 1 = 9

t = (Dbar - µd)/[Sd/sqrt(n)]

t = (2.3 – 0)/[ 2.1108/sqrt(10)]

t = 3.4457

The p-value by using t-table is given as below:

P-value = 0.0037

P-value < α = 0.01, 0.05, 0.10

So, we reject the null hypothesis at α = 0.01, 0.05, 0.10

There is sufficient evidence to conclude that Brand 1 golf balls are hit a smaller distance, on average, than Brand 2 golf balls.

Answer: c. Yes, since the p-value is less than 0.01.