Question

Find the minimum sample size necessary to be 99% confident that the population mean is within 3 units of the sample mean given that the population standard deviation is 29. (a) What is the critical value that corresponds to the given level of confidence? Round your answer to two decimals, and remember that critical values are always positive. ___2.58___ (b) What would be the minimum sample size needed? Round your answer up to the next integer.

Answer 1

Answer:

1) Critical value$Z_{\alpha /2} = 2.58$  

2) 622.0036

Explanation:

Given data:

confident interval is 99%

population mean is 3 units

standard deviation 29

$\alpha = 1 - 0.99 = 0.01$

$\alpha = 0.01$

Critical value$Z_{\alpha /2} = 2.58$  

From standard table of Z

b)

Minimum sample size $= (Z_{\alpha /2} \times \sigma / E)^2$

$= (2.58 \times (29 / 3))^2$

= 622.0036

= 623 (Rounded up to next integer)