You have just graduated with a post graduate degree in business and have obtaine

Question

You have just graduated with a post graduate degree in business and have obtained a position with a large manufacturing firm. The director of marketing has asked you to estimate the mean time required to complete a particular unit of the manufacturing process. A sample of 600 units yields a mean of 7.2 days. Since the population standard deviation is unknown, the sample standard deviation of s=1.9 days must be used. Calculate and interpret the 90 percent interval for the mean completion time for the manufacturing process. If this mean time is estimated to be in excess of 7 days, a new process will be implemented to reduce production costs. b) A construction firm was charged with inflating the expense vouchers it files for construction contracts with the federal government. The contract states that a certain type of job should average $1,150. In the interest of time, the directors of only 12 government agencies were called on to enter court testimony regarding the firm's vouchers. If a mean of $1,275 and a standard deviation of $235 are discovered from testimony, would a 95 percent confidence interval support the firm's legal case? Assume voucher amounts are normal.

Explanation / Answer

a) The 90% c.i=Xbar+-Z(s/sqrt N-1), where Xbar is sample mean, s is sample standard deviation and Z is Z score at alpha=0.10.

=7.1+-1.64(1.9/sqrt 600-1)

=6.97 to 7.23

With 90% confidence the true population mean is between 6.97 and 7.23 days.

b) The 95% c.i=Xbar+-t11,0.05*(s/sqrt n)

=1275+-2.201*(235/sqrt 12)

=1125.69 to 1424.31

The mean is within the interval, therefore, accept H0, the result is not significant at alpha=0.05. Thus, the confidence interval does not support the firm's legal case.

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