Scientists researched the emerging rate from pupa of monarch butterfly (Danaus p

Question

Scientists researched the emerging rate from pupa of monarch butterfly (Danaus plexippus) in Northern Florida. Many pupas of monarch died because of parasitoids (parasite insects, like wasps). They observed 1,000 pupas in the field, and 268 butterflies emerged from pupa (success), but 732 were dead (failure). We assume each pupa is independent and identical, so those survival processes can follow binomial distribution. Calculate the sample proportion of survived pupas, p cap. What is the best point estimator of the TRUE "p"? Calculate the sample proportion of dead pupas, q cap. What is the theoretical standard deviation of p cap? Assume each pupa's survival is a Bernoulli experiment. What is the standard error for p cap, sigma_p cap? What is the critical value Z_90 when the level of confidence is 90%? What is the margin of error of p, when the level of confidence is 90%? What is the 90% Confidence Intervals of p? Interpret (h). You want your estimate must be accurate within 0.5% (E = 0.005) of the true survival rate, p when the level of confidence is 90%. What is the minimum required sample size, n? Use p cap and q cap to calculate.

Explanation / Answer

(a) It is 268/1000 = 0.268

(b) 0.268

(c) 732/1000 = 0.732

(d) = (np(1 - p)) = (1000 * 0.268 * 0.732) = 14.01

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