Question

In designing the power system for a satellite, an engineer needs to determine the probability of early failure for the batteries powering the system. A random sample of batteries needs to be selected for testing for early failure. Those sampled batteries will all be of the same type, suitable for use in the satellite. The engineer wishes to find the sample size that will provide an estimate of the true proportion of batteries that do not fail too early, π, that will be within 0.05 of the population proportion with probability no less than 95%. Assume that the population of batteries is large.

(a) If π is initially assumed to be 0.5, find the engineer’s required sample size, explaining your reasoning.

(b) After testing the number of batteries found in (a), only 250 prove satisfactory. What is the point estimate of π? If this were the true value of π how many batteries were tested unnecessarily?

Answer 1

Answer:

Given that:

a) If is initially assumed to be o.5.Find the engineer's required sample size,explaing your reasoning

In designing the power system for a satelite , an engineer needs to determine the probability of early failure for the batteries powering the system.

margin of error E = 0.05

We know that

margine of error

b) After testing the number of batteries found in (a),only 250 prove satisfactory.What is the point estimate of ? If this were the true value of how many batteries were tested unnecessarly?