Question

In a sample of 56 bags of fertilizer, the average weight was found to be 17.2 lb with a standard deviation of 0.7. Give a point estimate for the population standard deviation of the weight of the bags of fertilizer. Round your answer to two decimal places, if necessary.

a) 0.71 lb
b) 0.72 lb
c) 0.73 lb
d) 0.74 lb

Answer 1

The point estimate for the population standard deviation of the weight of the bags of fertilizer is 0.73 lb, rounded to two decimal places if necessary.The correct option is c) 0.73 lb.

Step-by-step explanation:

In statistics, when we have a sample from a population, we use the sample data to estimate the population parameters. In this case, we have a sample of 56 bags of fertilizer with an average weight of 17.2 lb and a standard deviation of 0.7 lb.

The formula for estimating the population standard deviation from a sample standard deviation is:

population standard deviation = sample standard deviation sqrt(n / (n-1))

where n is the size of the sample.

Substituting our values into the formula:

population standard deviation = 0.7 sqrt(56 / (56-1))

population standard deviation = 0.73 lb, rounded to two decimal places if necessary.

This point estimate is useful because it provides an estimate for the true population parameter, which we cannot directly measure. It allows us to make informed decisions based on our sample data, and helps us to understand the variability in the population. However, it's important to remember that point estimates are not always exact, and there is a level of uncertainty associated with them due to sampling variability.

Therefore, The correct option is c) 0.73 lb.