7. In the waters around the American West Coast there is growing concern that th

Question

7. In the waters around the American West Coast there is growing concern that the lengths of Great White Sharks have increased. Assume that marine biologists have amassed a Great White Shark database and they know that the mean length is 15.96 ft with a standard deviation of 2.83 ft. Also assume that a team of scientists have recently caught five Great White Sharks and have measured their lengths. The measurements (in ft.) are: 10.45, 14.44, 9.54, 11.83, & 15.68 Test the null hypothesis that the mean of the sample of Shark lengths points to the known population Please provide a brief answer to this question: Given the results of the test, what might the scientists be concluding? (one or two sentences will do)

Explanation / Answer

Here' the exercise you need to do in order to prove/disprove claim of scientists:

The sample mean is given by : (10.45+14.44+9.54+11.83)/5 = 9.252

The population mean is 15.96

Stdev = 2.83

Ho: Mu = 15.96
Ha: Mu! = 15.96
Test statistic, t = (9.252-15.96)/(2.83/sqrt(5)) = -5.30

At a df of n-1=4, and alpa=0.05, we have -2.776 as t crtical value. Since our t value is much lesser than -2.776 we reject null hypothesis

We conclude that mean of the sample of shark lenghts doesn't point to the known population. Hence, the claim of the scientists the shark lengths points to the known population is FALSE.

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