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I need help convincing my wife that it is within reason I should expect to spend...

I need help convincing my wife that it is within reason I should expect to spend $1000 on a new bow. I believe the population mean to be greater than $1000. After researching 6 top bow manufacturers from the same dealer I came up with the following prices: 1,100, 1,000, 1,149, 999, 1,100, 999. Test this hypothesis at a 0.05 significance level.

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