A) A, B, C, D C) Null hypothesis is (rejected / not rejected) That is, you can s

Question

A) A, B, C, D C) Null hypothesis is (rejected / not rejected)
That is, you can state there is (proof/significant evidence/not enough evidence) to conclude that the (population mean/sample mean) of the new type of golf ball is (less than/greater than/equal to)
Sample A,Sample B,
766,755,
780,754,
796,748,
787,735,
749,748,
797,769,
766,791,
773,815,
771,762,
730,776,
789,793,
766,763,
760,793,
808,727,
788,724,
807,873,
752,780,
721,780,
792,707,
770,700,
818,731,
784,793,
756,789,
768,752,
814,775,
786,768,
791,759,
721,744,
772,714,
785,750
Sample A,Sample B,
766,755,
780,754,
796,748,
787,735,
749,748,
797,769,
766,791,
773,815,
771,762,
730,776,
789,793,
766,763,
760,793,
808,727,
788,724,
807,873,
752,780,
721,780,
792,707,
770,700,
818,731,
784,793,
756,789,
768,752,
814,775,
786,768,
791,759,
721,744,
772,714,
785,750
Driving Force is a golf ball manufacturer. Their R & D department have been developing a type of golf ball with a new dimpling pattern that is designed to increase the flight distance of the ball. They are at the testing stage and run an experiment to test the mean flight distance for the new type of ball compared to a standard one. A special device is used to fire the balls at a set force and angle A sample of 30 of the new balls (sample A) and 30 standard balls (sample B) are fired using the device and the distance travelled (in feet) is recorded for each ball Sample A 766 780 796 787 749 797 766 773 771 730 789 766 760 808 788 807 752 721 792 770 818 784 756 768 814 786 791 721 772 785 Sample B 755 754 748 735 748 769 791 815 762 776 793 763 793 727724 873 780 780 707 700 731 793 789 752 775 768 759 744 714 750 Conduct an appropriate one-tailed hypothesis test. Assume that the population variances are not equal a) From the following options, select the correct null and alternate hypotheses for this test: The correct null and alternate hypotheses for this test are: b) Calculate the test statistic. Give your answer to 3 decimal places c) At a significance level of 0.05, the null hypothesis is hat is, you can state that there is new type of golf ball is to conclude that the of the that of the standard golf bal

Explanation / Answer

(a) Here Hypothesises are

H0 : A = B

Ha : A > B

Option A is correect here.

(b)

Pooled standard deviation sp = sqrt [(s12 + s22)/2] = sqrt [24.762 + 34.892)/2] =  30.25

(b) Test statistic

t = (775.43 - 762.27)/[30.25 * sqrt (1/30 + 1/30)] = 1.686

(c) as t (critical) = t(58,0.05) = 1.672

the null hypothesis is rejected.

so at significance level 0.05, there is significant evidence that the population mean of the new type of golf ball is greater than the old ball.

Sample A Sample B 766 755 780 754 796 748 787 735 749 748 797 769 766 791 773 815 771 762 730 776 789 793 766 763 760 793 808 727 788 724 807 873 752 780 721 780 792 707 770 700 818 731 784 793 756 789 768 752 814 775 786 768 791 759 721 744 772 714 785 750 Average 775.43 762.27 Std. Dev. 24.76 34.89

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