Question

In: Statistics and Probability

A random sample of 110 light bulbs had a mean line of x̅=595 hours. Assume that...

A random sample of 110 light bulbs had a mean line of x̅=595 hours. Assume that σ=31 hours. Construct 90% confidence interval for the mean life μ, of all light bulbs of this type

z_0.11.282

z_0.05 1.645

z_0.025 1.960

z_0.01 2.326

z_0.005 2.576

Expert Solution

Given that,

= 595

= 31

n = 110

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

Margin of error = E = Z_/2* ( / $\sqrt$ n)

= 1.645* (31 / $\sqrt$ 110)

= 4.8622

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

- E < < + E

595 - 4.8622 < < 595 + 4.8622

590.1378< < 599.8622

(590.1378 , 599.8622 )

orchestra answered 2 years ago

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