Answer :
Answer:
416
Step-by-step explanation:
Given that tThe population standard deviation for the height of college basketball players is 3.4 inches
For 99%confidence interval since sigma (population standard deviatin) is known we can use Z critical value for 99% confidence
Z critical value = 2.58
Margin of error = 0.43 = 2.58* std error
So std error of sample mean = [tex]\frac{0.43}{2.58} \\=0.1667[/tex]
Std error is nothing but population std dev/square root of sample size
i.e.
[tex]0.1667=\frac{3.4}{\sqrt{n} } \\\sqrt{n} =\frac{3.4}{0.1667} \\=20.396[/tex]
n should be atleast 416
415 players were randomly selected for the survey.
C = 99% = 0.99
α = 1 - C = 1 - 0.99 = 0.01
α/2 = 0.005
The z score of α/2 equals to the z score of 0.495 (0.5 - 0.005) which is equal to 2.576
Given that the margin of error E = 0.43, and the standard deviation (σ) = 3.4, hence:
[tex]E=z_\frac{\alpha }{2}*\frac{\sigma}{\sqrt{n} } \\\\0.43=2.576*\frac{3.4}{\sqrt{n} } \\\\n=415[/tex]
Hence 415 players were randomly selected for the survey.
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