Driving Force is a golf ball manufacturer Their R D departm

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 40 of the new balls (sample A) and 40 standard balls (sample B) are fired using the device and the distance travelled (in feet) is recorded for each ball.

Download the data

Conduct a one-tailed hypothesis test for equality of the population means. Assume that the population variances are not equal.

You may find this Student\'s t distribution table useful.

a)From the following options, select the correct null and alternate hypotheses for this test:

A:H₀: u_A = u_B, H_a: u_A < u_B

B:H₀: u_A = u_B, H_a: u_A > u_B

C:H₀: u_A < u_B, H_a: u_A > u_B

D:H₀: u_A = u_B, H_a: u_A ? u_B

The correct null and alternate hypotheses for this test are: ABCD

b)Calculate the test statistic. Give your answer to 3 decimal places.

t =

c)At a significance level of 0.05, the null hypothesis is (rejected, not rejected).

That is, you can state that there is (proof, or significant evidence, or not enough evidence) to conclude that the (population mean flight distance or, sample mean flight distance) of the new type of golf ball is (less than, greater than, equal) to that of the standard golf ball.

Solution

(a) B:H₀: u_A = u_B, H_a: u_A > u_B

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(b)

t =1.594

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(c)not rejected

That is, you can state that there is not enough evidence to conclude that the population mean flight distance of the new type of golf ball is greater than to that of the standard golf ball.