A golf club manufacturer is testing a new design for a drive

A golf club manufacturer is testing a new design for a driver that is intended to produce longer drives as measured by the coefficient of the restitution for golf balls striking the club head. In a controlled experiment, the following values for coefficient of restitution were measured:

(a) Find the following:
sample mean
sample median
sample standard deviation
coefficient of variation

(b) Find a 95% confidence interval for the true mean coefficient of restitution for this type of club. State any necessary assumptions.

Solution

A golf club manufacturer is testing a new design for a driver that is intended to produce longer drives as measured by the coefficient of the restitution for golf balls striking the club head. In a controlled experiment, the following values for coefficient of restitution were measured:

0.8411

0.8191

0.8182

0.8125

0.8750

0.8580

0.8532

0.8483

0.8276

0.7983

(a) Find the following:
sample mean
sample median
sample standard deviation
coefficient of variation

count

10

mean

0.835130

sample standard deviation

0.023845

sample variance

0.000569

coefficient of variation (CV)

2.86%

median

0.834350

(b) Find a 95% confidence interval for the true mean coefficient of restitution for this type of club. State any necessary assumptions.

CI= \\bar x \\pm t *\\frac{s}{\\sqrt{n}}

t table value at 0.05 level of significance= 2.2622

CI =   0.835130 \\pm 2.2622 *\\frac{0.023845 }{\\sqrt{10}}

=(0.8181, 0.8522)

confidence interval 95.% lower

0.8181

confidence interval 95.% upper

0.8522

Assumptions: The data are random and independent and come from normal population. ( the population is normally distributed.)