Clinic I 1) The \"jumping seal\" lives in Coconut Island. Because this is an end

Question

Clinic I 1) The "jumping seal" lives in Coconut Island. Because this is an endangered species its population has been studied intensively Scientists have determined that the body size of adult jumping seals has a parametric mean of 1.83 m (measured from the tip of the snout to the tip of the tail) and a parametric standard deviation of 0.21 m. Recently, a single individual of jumping seal was found on a small island just south of Coconut Island. This single individual was very large, 2.13 m in length, and scientists think that this observation is very extreme. a) Calculate the probability of finding an individual as extreme in size (at least 2.13 m) as the one found in the small island. b) The observation of the large individual has prompted scientists to visit the small island to study its population and determine whether it's really different in body size relative to the population in Coconut Island. To be able to answer this question they sampled 9 individuals from the small island and calculated a sample average of 2.11 m and a standard deviation of 0.15 m. Use a 95% confidence interval to determine whether there is a real indication that the small island population has different parametric mean compared to the one in Coconut Island. c) Calculate a 95% CI for the population variance of the small island population. Does the interval suggest that the two populations have a difference in variability for size?

Explanation / Answer

A) P(X > 2.13) = P(X - mu) / sigma > (2.13 - 1.83)/0.21)

= P(Z > 1.43)

= 1 - P(Z < 1.43)

= 1 - 0.9236 = 0.0764

B) At 95% Confidence interval, the critical value Z0.975 = 1.96

The test statistic is,

Z = (x1 - x2) / sqrt ( Sd12/n1 + SD 22/n2)

= (2.11 - 1.83) / sqrt((0.15)2/9 + (0.21)2/9)

= 0.28/0.086 = 3.256

As, the test statistic value is greater than critical value, the null hypothesis will be rejected.

So there is a real indication that the small island population has different parametric mean compared to the one in Coconut island.

C) Confidence interval = mean +/- Z0.975 * SD/sqrt (n )

= 2.11 +/- 1.96 * 0.15/sqrt(9)

= 2.11 + /- 0.098

= 2.012, 2.208

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