Question

In: Statistics and Probability

An electrical firm manufactures light bulbs that have a length of life that is approximately normally...

An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed with an unknown standard deviation. If a sample of 30 bulbs has an average life of 780 hours and a sample standard deviation of 50 hours, find a 95% confidence interval for the population mean of all bulbs produced by this firm.

761.33 < µ < 798.67

764.49 < µ < 795.91

765.07 < µ < 794.93

768.02 < µ < 791.98

Solutions

Expert Solution

Solution :

Given that,

= 780

s = 50

n = 30

Degrees of freedom = df = n - 1 = 30 - 1 = 29

a ) At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

  / 2 = 0.05 / 2 = 0.025

t /2,df = t0.025,29 =2.045

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

= 2.045 * (50 / 30) = 18.668

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

- E < < + E

780 -18.668 < < 780 +18.668

761.33 < < 798.67


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