Answer to Question #245373 in Statistics and Probability for nieks

Question

Suppose we wish to design a study to investigate the effects of loud music on teenagers’ ability to concentrate. We know from previous studies that the standard deviation of time to complete this task is 3.4 minutes. How many subjects would be required to ensure with 90% confidence that the generated estimate is within 1 minute of the true mean time required?

Answer 1

Step 1

Given standard deviation ( s ) = 3.4 

Confidence interval ( c ) = 90 % 

Margin oferror ( E ) = 1

Step 2

α = 1 - 0.90 = 0.10 

|Z(0.05)|=1.645 (check standard normal table)

sample size ( n ) = $(\frac{Z\times s}{E})^2$

=$(\frac{1.645 \times3.4}{1})^2$

= 31.28165

n = 31.3 

Take n=32