Question

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?)

Answer 1

The responses to these question can be defined as follows:

Explanation:

`n = 16\\\\ \bar{x}= 73.7\\\\\sigma = 12\\\\a = 0.05\ or\ a = 0.10\\\\H_(o) \ : \mu = 68\\\\H_(a) \ : \mu \\eq 68\\\\a = 0.05\\\\`

critical values
`=\pm t0.025,15 = \pm 2.131\\\\`

`(n-1) = 15^(\circ)\\\\a = 0.10\\\\`

critical values
`= \pm t0.05,15 = \pm 1.753\\\\`

`(n-1) = 15^(\circ)\\\\`

Testing the statistic values:

`t = (x-\mu_(0))/( (s)/(√(n)))\\\\`

`= (73.7-68)/(((12)/(√(16))))\\\\\ = (5.7)/(((12)/(4)))\\\\ = (5.7)/((3))\\\\ = 1.9\\`

Test statistic ta
`= -1.90\ lies`

The critical values
`\pm t_(0.05,15) =\pm 1.753`

It is in the region of dismissal. We dismiss the 10% significant null hypothesis.

`t_a = 1.90 \\\\df = 15\\\\a = 0.05\\\\p-value = 076831\\\\`

P - value is greater than the level of significance a= 0.05

Null hypothesis we don't reject. At a 95% level, the claim is justified.

`t_a = 1.90\\\\ df = 15\\\\ a = 0.10\\\\p-value = 076831\\\\`

P - value below the meaning level a = 0.10, we reject the hypothesis null. At a level of 90% the claim is not justified.