Question

The lifetime of a certain brand of electric light bulb is known to have a standard deviation of 46 hours. Suppose that a random sample of 80 bulbs of this brand has a mean lifetime of 480 hours. Find a 90% confidence interval for the true mean lifetime of all light bulbs of this brand. Then complete the table below.

Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.)

What is the lower limit of the 90% confidence interval? What is the upper limit of the 90% confidence interval?

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 480

sample standard deviation = s = 46

sample size = n = 80

Degrees of freedom = df = n - 1 = 80-1= 79

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.9 = 0.1

/ 2 = 0.1 / 2 = 0.05

t /2,df = t0.05,79 = 1.664

Margin of error = E = t/2,df * (s /n)

= 1.664 * (46 / 80)

E = 8.558

The 90% confidence interval estimate of the population mean is,

- E < < + E

480 - 8.558 < < 480 + 8.558

471.4 < < 488.6

(471.4,488.6)

lower limit of the 90% confidence interval is 471.4

upper limit of the 90% confidence interval is 488.6