Old Design New Design 307 297 316 308 312 300 335 299 304 313 305 309 310 306 31

Question

Old Design New Design 307 297 316 308 312 300 335 299 304 313 305 309 310 306 313 301 330 316 315 296 321 298 304 301 319 300 312 319 324 291 298 306 308 285 310 324 329 299 303 303 298 301 295 309 302 298 313 303 304 297 303 285 281 306 320 302 280 314 300 301 306 301 308 281 314 295 307 304 306 292 295 302 309 319 309 294 318 290 307 286 Titleist, a company that manufactures golf balls, has come up with what they believe to be a revolutionary design idea that will reduce the variance in a golfer's drives. To test this claim, they recruit the world's number one ranked golfer, Jordan Spleth, to hit a bucket of balls of each type on the driving range. Jordan hits the bucket of old golf balls first and the bucket of golf balls with the new design second. He hits 30 golf balls with the old design and 50 with the old design. The manufacturer wants to perform the hypothesis test at the 1% level of significance. Use the data in Excel to test the company's claim that their old golf ball design has a larger variance than the new design. a. What type of test should be used here? Briefly explain why. b. Write the null and alternative hypotheses. c. Check the conditions to ensure that the test from part (a) is appropriate to use. d. Calculate the test statistic. (You may use Excel and just report the value, but be sure you can do the calculation by hand as well.) e. How many degrees of freedom does this test have? f. Use the Hypothesis Test Workbook to calculate the exact p-value. g. Will you reject or fail to reject the null hypothesis? Explain why using the critical value or p-value h. Write a conclusion in the context of the problem.

Explanation / Answer

a. Type of test : F- test must be used

Reason : Here we have to check the claim that of golf ball making company that it has produces less variance product. So, it is variance difference between two groups so F- test must be used.

b. H0 : There is no significant difference in variation between both type of balls.2old = 2New

H1: There is significant difference in variation between both type of balls and . 2old > 2New

c. Here we have provided two data sets from which we can calculate sum of square error and mean square error between both groups and within groups. So, these data sets are sufficient to do F test.

d. Test statistic

F = s1 2/ s2 2

where s12 and s22 and are the sample variances. The more this ratio deviates from 1, the stronger the evidence for unequal population variances.

by F- test , F* = (12.60)2/ (9.32)2 = 1.8265

and F critical = F,N11,N21 = F0.01, 29,49 = 2.1182

so F < Fcritical

so we can say that there is not significant difference between 2 variances.

e.Degrees of freedom this test have = 30 -1+ 50 -1 = 78

f. Hypothesis test to calculate p - value => p - value = 0.0308

g. I will not reject the null hypothesis as the given p- value is not under significance level. Reason why we choose critical value of p - value is to see what is the probability of variance under significant level.

h. We can see that new golf ball are not provided the result as mentioned by the gold making company. There is no substantial shift in variance between balls.

Related Questions

Navigate

• Browse (All)
• Browse O
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.