Question

In: Statistics and Probability

The US Navy is interested in acquiring a new communications relay for its submarines. Manufacturers tested...

The US Navy is interested in acquiring a new communications relay for its submarines. Manufacturers tested 50 units and found the mean time between failures to be 2607 minutes, and the sample standard deviation to be 675. Find a 95% CI for the mean time between failures. (Assume the sample comes from a normal population.)

Expert Solution

Solution :

Given that,

= 2607

s = 675

n = 50

Degrees of freedom = df = n - 1 = 50 - 1 = 49

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t_/2,df = t_0.025,49 = 2.010

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

= 2.010 * (675 / $\sqrt$ 50)

= 191.87

Margin of error = 191.87

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

- E < < + E

2607 - 191.87 < < 2607 + 191.87

2415.13 < < 2798.87

( 2415.13, 2798.87 )

orchestra answered 1 year ago

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