Question

4.) 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. 94.18 93.63 95.12 94.75 93.83 95.35 94.70 94.15 95.28 94.71 94.62 95.49 95.52 96.08 95.77 95.07 93.86 93.34 Source: Brooksbaseball.net 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. USE PANIC

PANIC = prameter , assumptions , name, interval, conclusion

Answer 1

Solution

Let X = pitch of a Clayton Kershaw four-seam fast ball

Given X ~ N(μ, σ²), where μ and σ are the mean and standard deviation of X.

100(1 - α) % Confidence Interval for population mean μ, when σ is not known is: Xbar ± MoE........... (1)

where

MoE = (t_{n- 1, α /2})s/√n ............................................................................................................................. (2)

with

Xbar = sample mean,

t_{n – 1, α /2} = upper (α/2)% point of t-distribution with (n - 1) degrees of freedom,

s = sample standard deviation and

n = sample size.

Calculations

n	18
Xbar	94.7472
s	0.7828
α	0.05
tα/2	2.1098
MoE	0.3893
Lower Limit	94.3580
Upper Limit	95.1365

So,

95% confidence interval for the mean pitch of a Clayton Kershaw four-seam fast ball is:

[94.3580, 95.1365] Answer

DONE