Mathematics: A sport analyst wants to determine the mean salary of a Baseball player for 2015. He believes an estimate of this average salary using a confidence interval is sufficient. How large a sample should he take to be within $497,000 of the actual average with 80% confidence? He calculates the standard deviation of salary for all baseball players for 2015 is about $5,478,384.55. Round your answer to whole number.

B as all angles in a triangle must add up to 180 10+120=130180-130=50 Therefore the last angle must be 50°...

A sport analyst wants to determine the mean salary

serehnatyras0808

29.01.2022

The large sample size 'n' = 199.6569≅ 200

Step-by-step explanation:

Step(i):-

Given Standard deviation of salary for all baseball players for 2015 is about $5,478,384.55

Standard deviation of of salary for all baseball players for 2015

(S.D ) σ = $5,478,384.55

Given estimate of this average salary for all baseball players for 2015

= $497,000

Given Margin of error of error is = $497,000

Level of significance ∝ = 80%

The critical value Z₀.₂₀ = 1.282

Step(ii):-

Margin of error of error is determined by

$M.E = \frac{Z_{0.20} S.D}{\sqrt{n} }$

$497,000 = \frac{1.282 X 5,478,384.55}{\sqrt{n} }$

Cross multiplication , we get

$\sqrt{n} = \frac{1.282 X 5,478,384.55}{497,000 }$

On calculation , we get

√n = 14.13

Squaring on both sides, we get

n = 199.6569

Conclusion:-

The large sample size 'n' = 199.6569≅ 200

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