Question

A random sample of 65 light bulbs had a mean life of = 1535 hours. Construct a 95% confidence interval for the mean life, μ, of all light bulbs of this type. Assume σ = 77 hours.

Group of answer choices

1516 hr < μ < 1554 hr

1519 hr < μ < 1551 hr

1521 hr < μ < 1549 hr

1510 hr < μ < 1560 hr

1514 hr < μ < 1556 hr

Answer 1

Solution :

Given that,

Point estimate = sample mean =     = 1535

Population standard deviation =    =77

Sample size n =65

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

Margin of error = E =   Z/2    * ( /n)
= 1.96* (77 / 65 )

= 19
At 95% confidence interval estimate of the population mean
is,

- E < < + E

1535- 19 <   < 1535+ 19

1516 hr < μ < 1554 hr