Question

A study of elephants is conducted to determine the average weight of a certain subspecies of elephants. The standard deviation for the population is 1000 pounds. At a 90% level, how many elephants need to be weighed so the average weight will be accurate to within 300 pounds?

Answer 1

To achieve a 90% confidence level that the average weight of the elephant subspecies is accurate within 300 pounds, one would need to sample approximately 301 elephants.

Step-by-step explanation:

The question is asking to calculate the sample size needed to estimate the average weight of a particular subspecies of elephants with a given precision and confidence level. To answer this, we use the formula for sample size in estimating a population mean with a known standard deviation:

n = (Z*σ/E)^2

Where n is the sample size, Z is the Z-value corresponding to the confidence level (for 90%, Z is approximately 1.645), σ is the population standard deviation, and E is the desired margin of error.

Plugging in the values given, we get:

n = (1.645*1000/300)^2

n ≈ (548.3)^2

n ≈ 300,689

So, rounding up, one would need to weigh 301 elephants to have a 90% confidence that the average weight will be accurate to within 300 pounds.