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We have developed a new mobile device and wish to gain insight into the price that...

We have developed a new mobile device and wish to gain insight into the price that prospective customers will pay for it. We ask 40 individuals how much they will pay, and calculate the average price and variance which come out to be 1,588 and 6,332 respectively. The 85% confidence interval is given by:

A. [1569.9,1606.1]

B. [1575.0,1601.0]

C. [1563.3,1612.7]

D. [146.8,3029.2]

math   Statistics-And-Probability   
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Answer #1

Confidence interval is (mean - z​​​​​​alpha/2*standard deviation/√n,mean + z​​​​​​alpha/2*standard deviation/√n)

Alpha= 0.15

Z​​​​​Zalpha/2= Z​​​​​​0.15/2 = Z​​​​​​0.075 = 1.44

Hence z​​​​​​alpha/2* standard deviation/√n

= 1.44*√6332/√40 = 18.11

Hence confidence interval is ( 1588- 18.11,1588+18.11)

=(1569.9,1606.1)  

Option A is the answer

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