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, thest the no action hypothesis that the balls have a mean distance of 295 yards.

a) The test statistic of 2.238 is greater than the critical value is 2.101 therefore HO is rejected. it is reasonable to assume that the distance is not 295 yards.

b) The test statistic of 3.003 and the critical value is 2.101, therefore the test statistic is greater than the critical value of 2.101 and the null hypothesis is rejected. The distance is not 295 yards

c) The test statistic of 1.908 is less than the critical value of 2.101 therefore HO is not in the area of rejection. It is reasonto assume that the distance is about 295 yards.

d) The test statistic is 1.297 and the critical value is 2.101 therefore the test statistic is less than the critical value and the null hypothesis is not rejected. The distance is about 295 yards.

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

Answer 1

GIVEN:

Sample size

I have used excel function to calculate mean and standard deviation of the given sample

To calculate Mean: "=AVERAGE(select array of data values of sample)"

To calculate Standard deviation: "=STDEV(select array of data values of sample)"

Sample mean

Sample standard deviation

The given problem is to test whether the the balls have a mean distance of 295 yards. Thus we use "One sample t test" to test this claim.

HYPOTHESIS:

The hypothesis is given by,

(That is, the mean distance of the balls is not significantly different from 295 yards.)

(That is, the mean distance of the balls is significantly different from 295 yards.)

LEVEL OF SIGNIFICANCE:

TEST STATISTIC:

which follows t distribution with degrees of freedom

CALCULATION:

CRITICAL VALUE:

The two tailed t critical value with degrees of freedom at significance level is .

DECISION RULE:

CONCLUSION:

Since the calculated value (-2.24) is less than the t critical value (-2.1009) we reject null hypothesis and conclude that the mean distance of the balls is significantly different from 295 yards.

The test statistic of -2.238 is less than the critical value is -2.101 therefore HO is rejected. it is reasonable to assume that the distance is not 295 yards.