Respuesta :
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.
[tex]n\geq (\frac{z_{\alpha/2}\cdot\sigma}{E})^2[/tex], where,
[tex]\sigma=\text{Standard deviation}=0.05[/tex],
[tex]\alpha=\text{Significance level}=1-0.95=0.05[/tex],
[tex]z_{\alpha/2}=\text{Critical value}=z_{0.025}=1.96[/tex].
[tex]E=\text{Margin of error}[/tex]
[tex]n=\text{Sample size}[/tex]
Substitute given values:
[tex]n\geq (\frac{z_{0.025}\cdot\sigma}{E})^2[/tex]
[tex]n\geq (\frac{1.96\cdot0.05}{0.01})^2[/tex]
[tex]n\geq (\frac{0.098}{0.01})^2[/tex]
[tex]n\geq (9.8)^2[/tex]
[tex]n\geq 96.04[/tex]
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.
