Here is the report about Par, Inc. , is a major manufacturer of golf equipment test whether the new ball drive longer distance than the current model. To compare the driving distances for the two balls, 40 simple tests both of new and current models were subjected to distance tests. According to the data, we got the information we need for a hypothesis test as follow: | Current| New| Means| 269. 42| 266. 67| Count | 40| 40| Standard Deviation| 8. 09| 9. 79| Confidence Level(95. 0%)| 2. 59| 3. 13| | | The 40 simple of both current and new model golf balls show that the average distance of the new ball drive is less than the current model, but the standard deviation of new ball is 9. 79 which is larger than the current one and It imply the new ball is not stable as the current one, it has more chance drive longer or shorter than the current model. But at present, we can’t get the conclusion which ball drive longer distance, So we need a hypothesis test the difference of this two ball models.
The hypothesis test suggested follows: H0:µ 1-µ 2? 0 Ha:µ 1-µ 2>0 We use this formula for a hypothesis test to compare the driving distance of the current and new golf balls. After analyses, we get the conclusion that we can’t reject the null hypothesis. Because this is a hypothesis test about two different populations, standard deviation of population is unknown and we use t-test and the p-value we got equals 0. 09 which is much bigger than the confidence level of 0. 05. So it is Type? error and we do not reject the null hypothesis.
And we recommend the company to use the new model, that there is more chance to drive longer distance. The confidence interval we got for each model and or the difference between the means of the two populations are given below: Current: 266. 83~272. 00 New:263. 54~269. 80 The difference between two populations: -1. 26~6. 74 As the interval show above, at the level of 95% confidence, the distance current ball can drive is between 266. 83 and 272. 00 and the new one can drive between 263. 54 and 269. 80.
And the new ball can drive longer distance till 6. 74 than the current one, but it is possible that the new ball drive shorter distance than the current till 1. 26. I think simple sizes for this test is not enough. Because the population of ball is very big and there are only 40 simples testing. We make assumption that the population of the ball is 1000 the simple size now is 5 and the proportion is 40/1000 and NP equals 1. 6, N (1-P) equals 38. 4. The NP is smaller than 5 so. We need more simple sizes to make the test much exactly.