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 concerned 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 below At α = 0.05, test the no action hypothesis that the balls have a mean distance of 295 yards.

Yards
290
272
277
287
274
305
288
297
307
284
272
280
293
279
303
295
292
289
279

Question options:

1:The test statistics of 2.238 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.

2:The 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.

3: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.

4: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. .The test statistics of 2.238 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.

Answer 1

Closest one is:

CALCULATIONS

The provided sample mean is and the sample standard deviation is s=10.84931345, and the sample size is n=19.

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: μ =295

Ha: μ ≠ 295

This corresponds to a two-tailed test, for which a t-test for one mean, with unknown population standard deviation will be used.

(2) Rejection Region

Based on the information provided, the significance level is α=0.05, and the critical value for a two-tailed test is tc​=2.101.

The rejection region for this two-tailed test is R={t:∣t∣>2.101}

(3) Test Statistics

The t-statistic is computed as follows:

(4) Decision about the null hypothesis

Since it is observed that ∣t∣=3.003>tc​=2.101, it is then concluded that the null hypothesis is rejected.

Using the P-value approach: The p-value is p=0.0076, and since p=0.0076<0.05, it is concluded that the null hypothesis is rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population mean μ is different than 295, at the 0.05 significance level.

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