Question

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

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.

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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]

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