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靜思

2008-12-06 2:29 am

The American Sugar Production Association wants to estimate the mean yearly sugar consumption. A sample of 16 people has a mean yearly consumption of 60 pounds with a standard deviation of 20 pounds.
1) what is the best estimate of the population mean?
2)Explain why we need to usse the t distribution. What assumption do you need to make ?
3)For 90% confidence interval, what is the value of t ?
4)Develop the 90%confidence interval for the population mean?
5) would it be reasonable to conclude that the population mean is 63 pounds??

回答 (1)

The Little Prince of Mathematics

2008-12-06 2:45 am

✔ 最佳答案

1) The best estimate of the population mean is the sample mean, that is 60 pounds.
2) The reason for the need of using t distribution is that the sample mean cannot totally reflect the population mean. It may deviate for a little bit.
Before we use t distribution, we need to assume that the sugar consumption is normally distributed.
3) From t table, the value of t is 1.753.
4) 90% confidence interval (60-1.753*20/sqrt[16],60+1.753*20/sqrt[16]) = (51.235, 68.765)
5) It may be reasonable as it lies on the 90% confidence interval.

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