The horned lizard shoots blood out of its eye as a form of defense. To understand if this defense mechanism improves their survival, biologists went to the field and collected data on 46 horned lizards. After making observations, the biologists recorded that 15 lizards did not survive predatory attack when shooting blood from the eye: Answer the following questions. Round the numbers to 3 decimal places. Don’t add units to your answer: Blank #1: p Blank #2: Upper 95% CI Blank #3: Lower 95% CI Blank #4: N Blank #5: 15 Blank #6: 0.327 Blank #7: 0.185
The Correct Answer and Explanation is:
To analyze the effectiveness of the horned lizard’s defense mechanism, we start by calculating the proportion of lizards that did not survive.
The proportion p is determined using the formula:
p = x/n
where x represents the number of lizards that did not survive and n represents the total number of observed lizards. Substituting the given values:
p = 15/46 = 0.326
Next, we calculate the 95% confidence interval (CI), which provides an estimate of the true proportion in the population. The confidence interval is computed using:
CI = p ± Z * sqrt((p * (1 – p)) / n)
where Z corresponds to the Z-score for a 95% confidence level, approximately 1.96.
First, determine the standard error (SE):
SE = sqrt((p * (1 – p)) / n) SE = sqrt((0.326 * 0.674) / 46) SE = sqrt(0.219524 / 46) SE = sqrt(0.004772) SE = 0.069
Now, compute the upper and lower limits of the confidence interval:
Upper 95% CI = p + Z * SE Upper 95% CI = 0.326 + 1.96 * 0.069 Upper 95% CI = 0.326 + 0.135 Upper 95% CI = 0.461
Lower 95% CI = p – Z * SE Lower 95% CI = 0.326 – 1.96 * 0.069 Lower 95% CI = 0.326 – 0.135 Lower 95% CI = 0.191
Now, let’s finalize the answer in the required format:
Blank #1: 0.326 Blank #2: 0.461 Blank #3: 0.191 Blank #4: 46 Blank #5: 15 Blank #6: 0.326 Blank #7: 0.191
These calculations provide insight into the survival probabilities of horned lizards utilizing this defense mechanism. The confidence interval suggests that the true proportion of lizards that do not survive is likely between 0.191 and 0.461. Since the upper bound remains relatively high, it indicates that shooting blood may not be a completely effective deterrent against predators. Future research could explore the conditions under which this mechanism succeeds or fails in repelling threats.
