Question

Question 10 15 pts A known mutation in the tree frogs is thought to be a result of water pollution, but it is not known how common the mutation is. The institute funding your research asks you to use your sample to estimate the proportion of Laotian wild tree frogs with this mutation. You observe the mutated gene in 9 of the 45 frogs in your dataset (hopefully recorded in column labeled 'omg'- for "observed mutant gene" - of your dataset). Use the dropdowns to select the correct answers: Construct a 95% CI for the population proportion, but first: The point estimate [Select) The critical value z* = [Select ] The standard error of Ô = [Select] Now, put it all together to state your point estimate and 95% CI: [Select)

Answer 1

Q10)

Point estimate = $\widehat{p}=\frac{9}{45}=0.2$

Critical value is given by: $Z_{\alpha/2}=Z_{0.05/2}=Z_{0.025}=1.96$

Also, Standard error of $\widehat{p}$ = $\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}=\sqrt{\frac{0.2(1-0.2)}{45}}=0.0596$

We know that 95% confidence interval for true proportion is given by:

$\\(\widehat{p}\pm Z_{0.05/2}\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}})\\ \\ (\widehat{p}\pm Z_{0.025}\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}})\\ \\ (0.2\pm (1.96)(0.0596))\\ \\ (0.2\pm 0.1168)\\ \\(0.0832,0.3168)$

Note- Dear student, as per Chegg's policy, the expert is advised to solve only the first question.