Question

Problem:
A random sample of 56 fluorescent light bulbs has a mean life of 645 hours with a standard deviation of 31 hours. Construct a 95% confidence interval for the population mean.

Question: DO WE USE A Z OR T SCORE? WHICH ONE AND WHY.

Post your responses in a diagonal manner

Answer 1

Solution :

Given that,

= 645 hours

s = 31 hours

n = 56

Degrees of freedom = df = n - 1 = 56 - 1 = 55

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

  / 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,90 = 2.004

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

= 2.004 * ( 31 / 56)

= 8.3

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

- E < < + E

645 - 8.3 < < 645 + 8.3

636.7 < < 653.3

(636.7, 663.3 )

T score confidence inerval used because Population random sample is not given.