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 = 53   s = 65

a) Construct a 95% confidence interval for μ, the mean time to react to a red light while talking on a cell phone. (Round your answers to three decimal places.)

(_________ , _________)

b) 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 = ?

Answer 1

Solution :

Given that,

A)Point estimate = sample mean = = 53

sample standard deviation = s = 65

sample size = n = 47

Degrees of freedom = df = n - 1 = 47 -1 = 46

t _/2,df = 2.01

Margin of error = E = t_/2,df * (s /n)

= 2.01* (65 / 47)

Margin of error = E = 19.085

The 95% confidence interval estimate of the population mean is,

- E < < + E

53-19.085 < <53+19.085

33.915 < < 72.085

(33.915,72.085)

B)

Margin of error = E = 7

Z_/2 = 1.96

sample size = n = [Z_/2* / E] ²

n = [ 1.96*65 /7 ]²

n = 331

Sample size = n = 331