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Math Help - Confidence level

  1. #1
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    Confidence level

    Scott wants to estimate the cost of a night at Los Angeles hotel. He called a random sample of 8 hotels and got a sample mean costs for one night of $145.00 with sample standard deviation 40 dollars.

    A) Find an 85 percent confidence interval for the population mean costs.

    B) What sample size does he need to say with 90 percent confidence that the sample mean is within 10 dollars of the population mean.

    Help please. Any direction would be much appreciated.
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  2. #2
    MHF Contributor matheagle's Avatar
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    Since n=8 is small you need normality and you must use a t distribution...

    The symmetric two-sided interval is \biggl(\bar X-t_{n-1,\alpha/2}{S\over \sqrt n} , \bar X+t_{n-1,\alpha/2}{S\over \sqrt n}\biggr).
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  3. #3
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    Thanks but I'm still confused I have been looking all over the web and in my text book for a similar problem that I could mirror. This is my last question and it's killing me. But thanks for the direction.
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  4. #4
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    Quote Originally Posted by jmsal View Post
    Thanks but I'm still confused I have been looking all over the web and in my text book for a similar problem that I could mirror. This is my last question and it's killing me. But thanks for the direction.
    What part of the general interval given to you are you confused about?
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