Question

In measuring reaction time, a psychologist estimates that a standard deviation is .05 seconds. How large a sample of measurements must he take in order to be 95% confident that the error in his estimate of mean reaction time will not exceed 0.01 seconds?

Answer 1

97

Explanation:

We are asked to find the size of sample to be 95% confident that the error in psychologist estimate of mean reaction time will not exceed 0.01 seconds.

We will use following formula to solve our given problem.

`n\geq ((z_(\alpha/2)\cdot\sigma)/(E))^2`, where,

`\sigma=\text{Standard deviation}=0.05`,

`\alpha=\text{Significance level}=1-0.95=0.05`,

`z_(\alpha/2)=\text{Critical value}=z_(0.025)=1.96`.

`E=\text{Margin of error}`

`n=\text{Sample size}`

Substitute given values:

`n\geq ((z_(0.025)\cdot\sigma)/(E))^2`

`n\geq ((1.96\cdot0.05)/(0.01))^2`

`n\geq ((0.098)/(0.01))^2`

`n\geq (9.8)^2`

`n\geq 96.04`

Therefore, the sample size must be 97 in order to be 95% confident that the error in his estimate of mean reaction time will not exceed 0.01 seconds.