The authors of a paper describe an experiment to evaluate the effect of using a

Question

The authors of a paper describe an experiment to evaluate the effect of using a cell phone on reaction time. Subjects were asked to perform a simulated driving task while talking on a cell phone. While performing this task, occasional red and green lights flashed on the computer screen. If a green light flashed, subjects were to continue driving, but if a red light flashed, subjects were to brake as quickly as possible. The reaction time (in msec) was recorded. The following summary statistics are based on a graph that appeared in the paper.

n = 47      

x = 525

s = 75

Suppose that the researchers wanted to estimate the mean reaction time to within 7 msec with 95% confidence. Using the sample standard deviation from the study described as a preliminary estimate of the standard deviation of reaction times, compute the required sample size. (Round your answer up to the nearest whole number.)

n = ?

I used the formula n= ((t critical value)(sample standard deviation / (B, margin of error))^2 however, 468 was the wrong answer. I got 2.02 as my t critical value.

Explanation / Answer

you are supposed to use normal distribution with z=1.96 and treat sample std deviation as an estimate for population std deviaiton.

therefore required sample size n=(z*std deviation/E)2 =(1.96*75/7)2 =~441

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