Answered

The population standard deviation for the height of college basketball players is 3.4 inches. If we want to estimate 99% confidence interval for the population mean height of these players with a 0.43 margin of error, how many randomly selected players must be surveyed? (Round up your answer to nearest whole number) Answer:

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.

Find out more at: https://brainly.com/question/15016913

Other Questions