Question

Clayton Kershaw of the Los Angeles Dodgers is one of the premier pitchers in baseball. His most popular pitch is a four-seam fastball. The data below represent the pitch speed ( in miles per hour) for a random sample of 18 of his four-seam fastballs pitches.

156 190) 147 173 159 181 162 130 101 147 113 109

Assume that the population of pitch speeds of Clayton Kershaw’s four-speeds are normally distributed.

Construct a 95% confidence interval for the mean pitch of a Clayton Kershaw four -seam fastball. Find the proportion parameter, assumptions, name and the interval.

Answer 1

Given,

The data is,

156	190	147	173	159	181
162	130	101	147	113	109

The sample mean is,

$\small \bar{x} = 147.33$

The sample standard deviation is,

$\small s = 28.817$

The confidence interval is given by,

$\small Confidence\; Interval = \bar{x} \pm t * \frac{s} {\sqrt{n}}$

where t(11df) for 95% Confidence is 2.2010(since the sample size is less than 30 we use t score)

$\small Confidence\; Interval = 147.33 \pm 2.20 * \frac{28.817} {\sqrt{12}}$

$\small Confidence\; Interval =[129.4208,165.2392]$

A 95% confidence interval for the mean pitch of a Clayton Kershaw four -seam fastball is,

[129.4208 , 165.2392]