Answer to Question #321392 in Statistics and Probability for Thanatos

Question

the barangay captain wants to conduct a study to estimate average playing time of children ages 7 to 12 he wants to be 99% confident that the sample mean will be within 15 minutes of the true mean. If he can approximate a population standard deviation by 40 minutes and assume an approximately normal distribution, how large a sample should he get?

Answer 1

The critical value for $\alpha = 0.01$ is $z_c = z_{1-\alpha/2} = 2.5758.$

$$E=z_c\dfrac{\sigma}{\sqrt{n}}=15/2$$

$$n\ge(\dfrac{2.5758(40)}{7.5})^2$$

$$n=189$$