Question

i need help with this problem. thank you

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. x525 s 65 n47 (a) Construct a 95% confidence interval for , the mean time to react to a red light while talking on a cell phone. (Round your answers to three decimal places.) Interpret a 95 % confidence interval for u, the mean time to react to a red light while talking on a cell phone. We are 95 % confident that the mean time to react to a red light while talking on a cell phone is between these two values. We are 95% confident that the true mean time to react to a green light while talking on a cell phone is directly in the middle of these two values. We are 95 % confident that the true mean time to react to a green light while talking on a cell phone is between these two values. There is a 95 % chance that the true mean time to react to a red light while talking on a cell phone is directly in the middile of these two values. There is a 95% chance that the true difference in the mean time to react to a red light while talking on a cell phone is directly in the middle of these two values. (b) What assumption must be made in order to generalize this confidence interval to the population of all drivers? O The assumption that the subjects of the experiment formed the population of drivers The assumption that the experiment captured the population of drivers. The assumption that the subjects of the experiment formed a random sample from the population of distracted drivers. O The assumption that the subjects of the experiment formed the population of distracted drivers. O The assumption that the subjects of the experiment formed a random sample from the population of drivers. (c) 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.)

Answer 1

a)
Xbar +- t * s/sqrt(n)

df =n-1 = 47-1 = 46
t = t.inv.2t(0.05,46) =
2.0129

(525 - 2.0129 * 65/sqrt(47) , 525 - 2.0129 * 65/sqrt(47))
= ( 505.915 , 544.085 )

Interpretation

option c)

b)

option E) is correct

c)

n = (z *sd/e)^2

= (1.96* 65/7)^2

= 331.24

=332 {try 331 if wrong}