Question

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

DATA

Yards
298
273
284
292
275
309
292
302
311
287
279
282
297
283
305
299
294
295
286

Please choose one of the following options:

A) Test statistic is 1.297 and the critical value is 1.734, therefore the test statistics is less than the critical value and the null hypothesis is not rejected. The distance is about 295 yards.

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

C) 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.

D) The test statistic of 2.238 is greater than the critical value of 1.734, therefore H) is rejected. It is reasonable to assume that the distance is not 295 yards.

Answer 1

Solution:

In R studio

Rcode:

Yards <- c(
298,
273,
284,
292,
275,
309,
292,
302,
311,
287,
279,
282,
297,
283,
305,
299,
294,
295,
286)
print(Yards)
length(Yards)
t.test(Yards,mu=295)

output:

One Sample t-test

data: Yards
t = -1.2967, df = 18, p-value = 0.2111
alternative hypothesis: true mean is not equal to 295
95 percent confidence interval:
286.4500 297.0237
sample estimates:
mean of x
291.7368

t= -1.2967,

p=0.2111

p>0.05,Do not reject Ho.

OPTION A

A) Test statistic is 1.297 and the critical value is 1.734, therefore the test statistics is less than the critical value and the null hypothesis is not rejected. The distance is about 295 yards.