Question

An auto mechanic knows the average time it takes to replace a defective car radiator is 70 minutes with a standard deviation of 12 minutes. This average is based on a random sample of 50. Which Excel statements will construct a 90% confidence interval for the time needed to replace a defective car radiator?

	a.	=70+1.96*12/SQRT(50), and =70-1.96*12/SQRT(50)
	b.	=70+1.96*3.46/SQRT(50), and =70-1.96*3.46/SQRT(50)
	c.	=70+1.645*3.46/SQRT(50), and =70-1.645*3.46/SQRT(50)
	d.	=70+1.645*12/SQRT(50), and =70-1.645*12/SQRT(50)
	e.	None of the above.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 70

Population standard deviation = = 12

Sample size = n = 50

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z _0.05 = 1.645

Confidence interval is = Z_/2* ( /n)

= 70 + 1.645 * (12 / 50) and 70 - 1.645 * (12 / 50)

d)