An aircraft maintenance company wants to find out how much time on average it ta

Question

An aircraft maintenance company wants to find out how much time on average it takes her employees to complete the assembly of a properly functioning airplane lavatory. (Clearly we are not referring to United Airlines). The manager examines the records of 9 prior assemblies and notes that it takes 11.5 hours complete the work. Assume that the standard deviation for all prior assemblies to be 2.3 hours.

a)      Construct a confidence inteval using the “standard” value for C.

b)     For future earnings analytics purposes, the company would like to reduce the margin of error of 0.25 hours. How many assembies would they need to examine in order to reduce the margin or error to this amount?

Explanation / Answer

here n=9 , sample mean=11.5, sd=2.3

standard value of C=confidence interval is taken 95%

(a) (1-alpha)*100% confidence interval for population mean=sample mean± z(alpha/2)*sd/sqrt(n)

95% confidence interval for population mean=11.5±z(0.05/2)*2.3/sqrt(9)=11.5±1.96*2.3/sqrt(9)=11.5±1.5=(10,13)

here we take standard value of C=95%

(b) with (1-alpha)*100% confidence margin of error= z(alpha/2)*sd/sqrt(n)

with 95% confidence margin of error= z(0.05/2)*2.3/sqrt(n)

or,0.25=1.96*2.3/sqrt(n)

or, sqrt(n)=1.96*2.3/0.25=18.032

or, n=325.15 ( next whole number is 326)

so answer is 326

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