contestada

scientist studying babies born prematurely would like to obtain an estimate for the mean birth weight, μ, of babies born during the 24th week of the gestation period. She plans to select a random sample of birth weights of such babies and use the mean of the sample to estimate μ. Assuming that the population of birth weights of babies born during the 24th week has a standard deviation of 2.8 pounds, what is the minimum sample size needed for the scientist to be 99% confident that her estimate is within 0.5 pounds of μ?Carry your intermediate computations to at least three decimal places. Write your answer as a whole number (and make sure that it is the minimum whole number that satisfies the re

Respuesta :

ANSWER:

209

STEP-BY-STEP EXPLANATION:

The statement gives us the margin of error (E = 0.5) and the standard deviation (σ = 2.8).

For 99% confidence level, z value is 2.58 as P(-2.58 < z < 2.58 ) = 0.99

With the following formula we can then determine the minimum value of the sample size:

[tex]\begin{gathered} E=Z_c\cdot\frac{\sigma}{\sqrt{n}} \\ \\ \text{ We replacing:} \\ \\ 0.5=2.58\cdot\frac{2.8}{\sqrt{n}} \\ \\ \sqrt{n}=\frac{2.58\cdot2.8}{0.5} \\ \\ n=\left(\frac{2.58\cdot2.8}{0.5}\right)^2 \\ \\ n=208.74\approx209 \end{gathered}[/tex]

The minimum sample size needed es 209

Otras preguntas