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Question 1. 1. [30 pts]) The United Federation of Planets' shipyards on Utopia Planitia report that they can replicate dilithium coils with a claimed warp

Question 1.

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1. [30 pts]) The United Federation of Planets' shipyards on Utopia Planitia report that they can replicate dilithium coils with a claimed warp phase flux of 68 cochranes. a.(15) In order to justify this claim for the Ferengi a sample of 16 coils is taken. For this sample set, the mean warp phase flux is found to be 73.7 cochranes with a sample measured standard deviation of 12 cochranes. Is this claim justified at the two-sided 95% or 90% levels? (Derive and define the appropriate values to show true or false for each of the levels. Eg. Is the found mean within the allowed range?) b.(15) In order to justify this claim for the Vulcans a sample of 144 coils is taken. For this sample set, the mean warp phase flux is found to be 66.5 cochranes with a true probabilistically defined standard deviation of 9 cochranes. Is this claim justified at the two-sided 95% or 90% levels? (Derive and define the appropriate values to show true or false for each of the levels. Eg. Is the found mean within the allowed range?)

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