Question

A psychologist estimates the standard deviation of a driver's reaction time to be 0.05 seconds. How large a sample of measurements must be taken to derive a confidence interval for the mean with a margin of error at most 0.01 second, and confidence level 95%?

Answer 1

Answer: 97

Explanation:

The formula to find the sample size:-

`n=((z^*\cdot \sigma)/(E))^2` , where
`\sigma` = prior standard deviation., z^*= Critical value corresponds to the confidence level and E is margin of error .

Given : A psychologist estimates the standard deviation of a driver's reaction time to be 0.05 seconds.

i.e.
`\sigma=0.05`

E= 0.01

Critical value for 95% confidence interval = 1.96

Then, the required sample size will be

`n=((1.96*0.05)/(0.01))^2\\\\n=(1.96*5)^2\\\\ n=9.8^2=96.04\approx97` [Round to the nest integer.]

Hence, the required minimum sample size = 97