Question

6. Suppose it is needed to estimate the number of turtles in a lake. One day a sample of 300 turtles are captured, marked, and released back into the lake. The following day a sample of 150 turtles are captured, of which 69 of them are marked (and so recaptured). (a) Estimate the number of turtles in the lake. [Show some work.] (5) (b) Give a 95 percent interval estimate for that in Part (a). [Show some work.] (5)

Answer 1

a) The estimate the number of turtles in the lake is ,

$\hat{p}=\frac{X}{n}=\frac{69}{150}=0.46$

b) The 95% confidence interval estimate for the proportion of turtles in the lake is ,

$\hat{p}\pm Z_{\alpha/2}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$

$0.46\pm 1.96*\sqrt{\frac{0.46(1-0.46)}{150}}$ ; $Z_{\alpha/2}=Z_{0.05/2}=1.96$ , From Z-table

$0.46\pm 0.0799$