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A survey of 170 commuters shows that on average people travel 17.4 km with standard deviation...

A survey of 170 commuters shows that on average people travel 17.4 km with standard deviation 8.4 km. Find 99% confidence interval for the population mean commuting distance. State your conclusion.

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Answer #1

Solution :

Given that,

Point estimate = sample mean = = 17.4


Population standard deviation =    = 8.4

Sample size = n =170

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576   ( Using z table )

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

= 2.576* ( 8.4/ 170)

E= 1.6596

At 99% confidence interval estimate of the population mean is,

- E < < + E

17.4 - 1.6596< < 17.4+1.6596

15.7404< < 19.0596

(15.7404,19.0596)

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