# Statistics- Assume that your firm, Daulton & Weed, CPAs

| February 25, 2017

Question
Assume that your firm, Daulton & Weed, CPAs, has been approached by a Tempest, a golf ball manufacturer, to attest to the average drive distance that Tempest’s new GOFAR ball can be driven. Tempest has presented you the following four possible assertions:
The GOFAR ball goes an average of X yards when hit by LongBall, a mechanical golf ball hitting machine with a precision of + 1 yard.
The GOFAR ball goes an average of X yards when hit by LongBall, a mechanical golf ball hitting machine with a precision of + 2 yards.
The GOFAR ball goes an average of X yards when hit with a driver by a random group of amateur golfers with a precision of + 1 yard.
The GOFAR ball goes an average of X yards when hit with a driver by a random group of amateur golfers with a precision of + 2 yards.
You have been provided the following table of results of prior tests of the GOFAR golf ball by the company.

LongBall

Amateur Golfer

Average Distance

320 Yards

240 yards

Standard Deviation

6 yards

16 Yards

You have determined that to attest to the assertion you would have to be 95 percent (1.96 coefficients) confident that the average distance is within the precision specified. You are aware that the required sample size to estimate the mean of a population is:

Sample size = (Coefficient for conf. level × Std. dev)²
———————————————–
Desired Precision

Required:

Calculate the required sample size for each of the four assertions using classical variables sampling.
Discuss the effects of the following factors on the required sample size:
Standard deviation.
Level of precision.

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