5. An experiment is designed to measure the time necessary for a robotic lens to

Question

5. An experiment is designed to measure the time necessary for a robotic lens to adapt to reduced light, we have n=50 observations from the repeated experiments. The sample mean, X, was 6.32 seconds and the sample standard deviation, s, was 1.65 seconds. a. Using the central limit theorem, what approximate distribution does follow where is the true population mean and is the true population standard deviation? b. Compute an approximate 95 percent confidence interval for the true average adaptation time

Explanation / Answer

a. It follows a normal distribution

b.

Standard error of the mean = SEM = S/N = 0.233

t(, N-1) = 2.01

Confidence interval = m +/- (t(, N-1)*SEM)

Mean = 6.23

Lower bound: 5.76

Upper bound: 6.7

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