Question

The Lawnpoke Golf Association (LGA) has established rules that manufactures of golf equipment must meet for their products to be acceptable for LGA events. BatOutaHell Balls uses proprietary process to produce balls with mean distances of 295 yards. BatOutaHell is concerned that is the mean distance falls below 295 yards, the word will get out and sales will sage. Further, if the mean distance exceeds 295 yards, their balls may be rejected by LGA. Measurements of the distances are recorded in DATA. At ∝ =0.05, test the no action hypothesis that the balls have a mean distance of 295 yards.

Yards 293 275 280 290 273 306 287 301 309 285 274 282 294 283 304 297 294 290 283

A.The test statistic is 3.003 and the critical value is 1.734, therefore the test statistic is greater than the critical value of 1.734 and the null hypothesis is rejected. The distance is not 295 yards

B. The test statistic is 1.297 and the critical value is 1.734, therefore the test statistic is less than the critical value of 1.734 and the null hypothesis is not rejected. The distance is about 295 yards

C. The test statistics is 2.238 is greater than the critical value is 1.734, therefore H0 is rejected. It is reasonable to assume that the distance is not 295 yards.

D. The test statistic is 1.908 is greater than the critical value is 1.734, therefore H0 is rejected. It is reasonable to assume that the distance is not 295 yards.

Answer 1

Sol:

Ho=mu=295

Ha:mu not =295

alpha=0.05

Rcode to get t and p value

distance_yards <- c(293, 275, 280 ,290 ,273, 306 ,287, 301 ,309, 285,
274, 282, 294 ,283, 304, 297, 294 ,290, 283)

t.test(distance_yards,mu=295)

Output;

One Sample t-test

data: distance_yards
t = -2.2383, df = 18, p-value = 0.03808
alternative hypothesis: true mean is not equal to 295
95 percent confidence interval:
284.2866 294.6608
sample estimates:
mean of x
289.4737

From output:

t=-2.2383

p=0.03808

p<0.05

Reject null hypothesis.

MARK

C. The test statistics is 2.238 is greater than the critical value is 1.734, therefore H0 is rejected. It is reasonable to assume that the distance is not 295 yards.