Government officials in Canberra have recently expressed concern regarding overr

Question

Government officials in Canberra have recently expressed concern regarding overruns on military contracts. These unplanned expenditures have been costing Australians millions of dollars every year. The' minister impanels a committee of experts to estimate the average amount each contract costs the government over and above the amount agreed upon. The committee has already determined that the standard deviation in overruns is $17.5 million, and that they appear normally distributed. If a sample of 25 contracts is selected, how likely is it the sample will overestimate the population mean by more than $10 million? The' minister will accept an error of $5 million in the estimate of mu. How likely is he to receive an estimate from the committee within the specified range?

Explanation / Answer

1) Since n is small, calculate t statistic. We have t = 10/(17.5/sqrt(25)) = 2.857 with df = 25-1=24 we have p value between 0.005 and 0.0005 from the T tables. So, you are likely to overestimate by more than 1-0.005 Therefore,

> 0.995

2) FOr specified range, t value = 5/(17.5/sqrt(25)) = 1.428. Referring to t table with df=25 we have P value between 0.05 and 0.1

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