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

(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.)

a) The 99% confidence interval would be given by (24.409;24.979)  

b) n=464

Step-by-step explanation:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

Part a

The confidence interval for the mean is given by the following formula:  

(1)  

In order to calculate the critical value we need to find first the degrees of freedom, given by:  

Since the Confidence is 0.95 or 95%, the value of and , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,46)".And we see that  

Now we have everything in order to replace into formula (1):  

So on this case the 95% confidence interval would be given by (503.01;546.99)

Part b

The margin of error is given by this formula:  

(1)  

And on this case we have that ME =7 msec, we are interested in order to find the value of n, if we solve n from equation (1) we got:  

(2)  

The critical value for 95% of confidence interval is provided, from part a, replacing into formula (2) we got:  

So the answer for this case would be n=464 rounded up to the nearest integer  

10 glasses of juice could be made with 5 carrots, 1,500 orange juice, 2,000 papaya juice.