Question

In a random sample of 450 light bulbs, 150 of them burned out in less than 1000 hours. For those light bulbs:

1. Estimate the value of the population proportion. (Round your answers to 3 decimal places.)

Population proportion:……?

2. Develop a 95% confidence interval for the population proportion. (Round your answers to 3 decimal places.)

Confidence interval:……? and …..?

Answer 1

Solution :

Given that,

n = 450

x = 150

Point estimate = sample proportion = = x / n = 150 / 450 = 0.333

1 - = 1 - 0.333 = 0.667

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025 = 1.960

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 1.960 (((0.333 * 0.667 ) / 450)

= 0.044

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.333 - 0.044 < p < 0.333 + 0.044

0.289 < p < 0.377

( 0.289 , 0.377 )

The 95% confidence interval for the population proportion p is : - ( 0.289 and 0.377 )