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 = 48      

x = 530

      s = 70

(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.)

(_____,_____)  

1a) Interpret a 95% confidence interval for μ, the mean time to react to a red light while talking on a cell phone.

A. 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. 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.    

C. 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.

D. 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 middle of these two values.

E. 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.

2 What assumption must be made in order to generalize this confidence interval to the population of all drivers?

a The assumption that the subjects of the experiment formed the population of drivers.

b The assumption that the experiment captured the population of drivers.    

c The assumption that the subjects of the experiment formed the population of distracted drivers.

d The assumption that the subjects of the experiment formed a random sample from the population of distracted drivers.

e 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 5 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-A:

n=48

df=n-1=48-1=47

alpha=0.05

alpha/2=0.05/2=0.025

t critical in excel

=T.INV(0.025,47)

=2.01174

95% confidence interval for mean is

xbar-t*s/sqrt(n),xbar+t*s/sqrt(n)

530-2.01174*70/sqrt(48),530+2.01174*70/sqrt(48)

509.6741,550.3259

509.674<mu<550.326

(509.674,550.326)

Solution-b:

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.

Solution=c:

n=(Z*s/MOE^2

=(2.576*70/5)^2

= 1300.612

n=1301

the required sample size.,n=1301