Question

The overall distance traveled by a golf ball is tested by hitting the ball with Iron Byron, a mechanical golfer with a swing that is said to emulate the legendary champion, Byron Nelson. Ten randomly selected balls of two brands are tested and the overall distance measured. Assume the data are normally distributed. The data follow: Brand i Brand 2 271 286 287 271 283 271 279 275 263 267 276 259 260 265 273 281 271 270 263 268 (a) Is there evidence to show that there is a difference in the variance of the brands? Use a = 0.05. (b) Calculate a 95% two-sided confidence interval on 01/02. Round your answer to three decimal places (e.g. 98.765). 10.4615 -0.461 13.861

Answer 1

A.

s1 =

s2 =

n1 = n2 = 10

Ho:o = oz Ha : 0=o

The F-statistic is computed as follows: 5195 66.68 49.6 = 1.344

Critical F-region:

R={F:F<0.248 or F > 4.026).

Since F = 1.344 lies in between the 0.248 and 4.026 thus we fail to reject H0 and thus there is no difference in the variance of brands.

B.

The critical values for a = 0.05 and df = n1 -1 = 10 – 1 = 9 and df2 = n2 - 1 = 10 - 1=9 degrees of freedom are: F1 = F1-a/2,12–1,12–1 = F1-0.05/2,10–1,10–1 = 0.2484 Fu = F/2,12-1,0-1 = F0.05/2.10–1,10–1 = 4.026 The corresponding 95% confidence interval is computed as follows: C1 = (* F-a2n-1m , Falpen-in-1) (8.1662 8.1662 70132 X F1-0.05/2,10-1,10-1, 70132 X F0.05/2,10-1,10-1 (8.1662 7.0432 X 84 8.1662 7.0432 X 4.026 = (0.3339, 5.4122)

The above confidence interval is for the ratio of variances, for std. deviation it is:

V0.3339, V5.4122

[0.578, 2.326]

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