Question

1. The time it takes a driver to react to the brake lights of a decelerating vehicle follows a normal probability distribution. A study was performed on reaction time and the data for a sample of 10 drivers is given below. Based on the following data:

1.09 0.88 0.52 1.48 1.38 1.27 0.64 1.77 1.41 1.11

1. Calculate the 99% confidence interval for the true average reaction time. Is 1.25 a reasonable possibility for the true mean value?
2. Predict the resulting reaction time resulting from a future study of a single individual by calculating the 95% prediction interval
3. Calculate an interval on which 90% of all values of the underlying population will be within at a certainty level of 95%.

Answer 1

First we need to find the mean and SD of data set. Following table shows the calculations:

	X	(X-mean)^2
	1.09	0.004225
	0.88	0.075625
	0.52	0.403225
	1.48	0.105625
	1.38	0.050625
	1.27	0.013225
	0.64	0.265225
	1.77	0.378225
	1.41	0.065025
	1.11	0.002025
Total	11.55	1.36305

Since confidence interval contains 1.25 so 1.25 is a reasonable possibility for the true mean value.

(b)

Since there 10 data values in the sample so degree of freedom is df=10-1=9 and critical value of t for 95% confidence interval, using excel function "=TINV(0.05,9)" is 2.262.
The 95% prediction interval is

Hence,

(c)

Value of k for 90% tolerance interval and 95% confidence interval is 2.839.

So requried tolerance interval is