AP Statistics Final Project

AP Statistics Final Project

Conditions

Not all the conditions for inference were met, but I still proceeded with a 2-Sample T-test.

• The groups were independent of one another. The mean distance of a ProV1 ball did not affect the mean distance of a Warbird.

• The two golf balls were not randomly selected from the population of that brand. A convenience sampling method was used, but it can still be inferred the balls used are representative of all golf balls of that brand.

• The distance hit in one trial cannot be proven to be independent of another trial, because changes and adjustments to the golfer’s swing take place between trials. If I wanted trials to be independent, I could have used a machine instead of a person to hit the golf balls.

• Sample size of golf balls is less than 10% of the population of that brand.

• Histograms of population are approximately normally distributed with removal of the outlier in data for the ProV1.

After gathering all the data, I could use a 2-Sample T-test to find if there was a significant difference in the distance hit

After computing the data:

t = -.0345

df = 16.8

x1 = 213.267

x2 = 213.39

p = .97285

Now to calculate the deviation from the fairway...

Histograms

Hypotheses

With a p-value of .972, far above our α = .01 significance level, we fail to reject the null hypothesis that there is no significant difference in the distance hit between golf balls. It cannot be concluded one ball hits significantly further than the other.

H0 There is no significant difference for the distance hit between the two golf balls

μProV1 – μWarbird = 0

HA There is a significant difference for the distance hit between the two golf balls

μProV1 ≠ = μWarbird

H0 There is no significant difference for the deviation from the fairway between the two golf balls

μProV1 – μWarbird= 0

HA There is a significant difference for the deviation from the fairway between the two golf balls

μProV1 ≠ μWarbird

Why use a 2-Sample T-test?

Data

Golf with my grandfather

• Compare the means of 2 samples
• Find if there is a significant difference between the two based on a p-value.
• t-values can account for the increased variability of a small sample size

After Joy hit 20 shots, 10 with each ball, we recorded the data from the simulator's computer.

Distance (yards)

Deviation from fairway (feet)

ClubGolf™

One of the most enjoyable things to do with my grandfather is golf. Although I never win, I always have a great time golfing with him. My grandfather and I are very specific about the type of ball we like to use. I use a Callaway Warbird ball and my grandfather uses a Titleist ProV1. The purpose of my experiment is to see which ball is actually better.

Conditions

Titleist ProV1

212.9

Outlier 162.9

197.3

223.9

216.7

205.6

217.6

214.7

217.9

212.8

Titleist ProV1

51.3

Outlier 238.5

32.1

61.5

48.6

22.9

90.4

43.9

112.5

16.0

Callaway Warbird

16.4

0.3

39.4

12.6

1.3

63.5

25.3

56.9

2.1

68.7

Callaway Warbird

204.4

213.3

200.1

219.2

220.9

207.8

209.9

216.3

224.9

217.1

My grandfather is a member at ClubGolf™, an indoor performance center that helps members to develop golf skills through the use of shot simulators, indoor greens, and lessons from golf professionals. My grandfather asked the pro he works with (an unbiased golfer) if she help in the experiment, without complete knowledge of what we were actually testing (single blinding). Her swing is also more consistent than an amateur golfer, which helped decrease the variability of our sampling.

Outliers were determined based on a value greater that 3Q plus 1.5xIQR or a value less than

1Q-1.5xIQR. Outliers were not used in the final calculations.

What type of hypothesis test?

Not all the conditions for inference were met, but I still proceeded with a 2-Sample T-test.

• The groups were independent of one another. The mean deviation of a ProV1 ball did not affect the mean deviation of a Warbird.

• The two golf balls were not randomly selected from the population of that brand. A convenience sampling method was used, but it can still be inferred the balls used are representative of all golf balls of that brand.

• The distance hit in one trial cannot be proven to be independent of another trial, because changes and adjustments to the golfer’s swing take place between trials. If I wanted trials to be independent, I could have used a machine instead of a person to hit the golf balls.

• Sample size of golf balls is less than 10% of the population of that brand

• Histograms of population are not normally distributed and in fact skewed to the right. There is one outlier in the data for the ProV1.

Analysis of Data

• Find which ball hits farther and which is more accurate
• Two 2-Sample T-test
• Hit 10 shots using each golf ball and measure distance traveled as well as deviation from the center of the fairway.
• One 2-Sample T-test to find if there is a significant difference in distance, and another test if there is a significant difference in the deviation.

Experimental Design

Histograms

• Clear that neither the ProV1 nor Callaway Warbird perform better than the other
• Both p-values > α = .01
• An α = .01 significance level was chosen for this experiment instead of the typical α = .05 because I could not assume the independence between swings.
• Had to have very convincing evidence
• Lowing α level, I decreased the probability of a Type I error as well as the power of the test, but increased the probability of a Type II error.

Conclusion

• Obtained a Titleist ProV1 and Callaway Warbird golf ball (suitable to be representative of all balls of that brand).
• Golf shot simulator
• Had Joy, the golf pro, hit 10 shots with the ProV1 and 10 shots with the Warbird
• Driver used throughout experiment
• Due to distinguishable honeycomb patterns between the two golf balls, we could not visual blinding

After computing the data:

t = 1.8336

df = 15.86

x1 = 53.244

x2 = 28.65

p = .0855

Titleist ProV1 golf balls are one of the most expensive golf balls, costing $39.99 per dozen, twice the cost of Callaway Warbird balls. Before I began this experiment, I hoped my data would prove there is no difference in the quality of the two golf balls and that ProV1 balls aren’t worth the extra money. I did prove this, but now instead of feeling satisfied, I realize I lose to my grandfather not because of the ball he uses, but because he is the better golfer.

With a p-value of .0855, above our α = .01 significance level, we fail to reject the null hypothesis that there is no significant difference in the deviation from the fairway between golf balls. There is no significant evidence that one ball is more accurate than another.

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