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

Answer:

97

Step-by-step 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.

$n\geq (\frac{z_{\alpha/2}\cdot\sigma}{E})^2$, 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:

$n\geq (\frac{z_{0.025}\cdot\sigma}{E})^2$

$n\geq (\frac{1.96\cdot0.05}{0.01})^2$

$n\geq (\frac{0.098}{0.01})^2$

$n\geq (9.8)^2$

$n\geq 96.04$

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.