4. A researcher is looking at the relative abundance of microbiota in the guts o

Question

4. A researcher is looking at the relative abundance of microbiota in the guts of wild chimpanzees in Cameroon. He randomly selects 25 chimpanzees from the population and analyzes their fecal samples for microbiota abundance. The data is below. Relative abundanco microbiota 0.08 0.12 0.23 0.11 0.13 0.22 0.08 0.11 0.15 0.18 0.09 0.10 Chimp ID # 6 8 9 10 13 14 15 16 17 18 19 20 21 · 0.20 0.20 0.20 0.12 0.19 0.17 0.20 0.18 0,05 0.09 0.14 23 24 25 0.16 Given alpha 0.01, perform a hypothesis test to address each of the following questions. Remember to define Ho and Ha, compute the test statistic, define the reject region, estimate the p-value and then state the conclusion. Is the population mean of mi

Explanation / Answer

H0 : = 0.15

Ha : 0.15

Sample mean x = 0.1488

Sample standard deviation s = 0.052

standard error of the sample mean se0 = 0.052/ 5 = 0.0104

Test Statistic

t = (0.1488 - 0.15)/ (0.052/ sqrt(25) = -0.0012/ 0.0104 = 0.12

Reject Region :

95% CI

x +- t24,0.05  se0 = 0.1488 +- 2.064 * 0.0104 = (0.127, 0.170)

reject region : reject region is t > tcr which t > 2.064

p - value = 2 * Pr (t > 2.064) = 0.9055

we shalln't reject the null hypothesis and can conclude that population mean of microbiota relative abundance is not different from 0.15.

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