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Sunny_sXe [5.5K]
3 years ago
14

In measuring reaction time, a psychologist estimates that a standard deviation is .05 seconds. How large a sample of measurement

s 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?
Mathematics
1 answer:
blondinia [14]3 years ago
5 0

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.

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