Question

Automobile manufacturers are interested in the difference in reaction times for drivers reacting to traditional incandescent lights and to LED lights. A sample of 7 drivers are told to press a button as soon as they see a light flash in front of them and the reaction time was measured in milliseconds. Each driver was shown each type of light. The average difference between the two reaction times (traditional - LED) was 66.893 ms with a standard deviation of 32.1985 ms. Calculate a 95% confidence interval for the average difference in reaction times to the two types of light for all drivers.

Question 9 options:

	1) (38.1158, 95.6702)
	2) (37.1144, 96.6716)
	3) (-37.1144, 96.6716)
	4) (54.7231, 79.0629)
	5) (64.4461, 69.3399)

Answer 1

Solution :

Given that,

Point estimate = sample mean = $\bar x$ = 66.893

sample standard deviation = s = 32.1985

sample size = n = 7

Degrees of freedom = df = n - 1 = 6

At 95% confidence level the t is ,

$\alpha$ = 1 - 95% = 1 - 0.95 = 0.05

$\alpha$ / 2 = 0.05 / 2 = 0.025

t_{$\alpha$ /2,df} = t_0.025,6 = 2.4469

Margin of error = E = t_{$\alpha$/2,df} * (s /$\sqrt$n)

= 2.4469 * (32.1985 / $\sqrt$ 7)

= 29.7786

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

$\bar x$ - E < $\mu$ < $\bar x$ + E

66.893 - 29.7786 < $\mu$ < 66.893 + 29.7786

37.1144 < $\mu$ < 96.6716

(37.1144 , 96.6716)

Option 2) is correct.