Question

In a sample of 83 walking canes, the average length was found to be 34.9in. with a standard deviation of 1.5. Give a point estimate for the population standard deviation of the length of the walking canes. Round your answer to two decimal places, if necessary.

Answer 1

The point estimate for the population standard deviation of the length of the walking canes is 0.16.

Explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean
`\mu` and standard deviation
`\sigma`, a large sample size can be approximated to a normal distribution with mean
`\mu` and standard deviation
`(\sigma)/(√(n))`.

In this problem

The point estimate of the standard deviation is the standard deviation of the sample.

In a sample of 83 walking canes, the average length was found to be 34.9in. with a standard deviation of 1.5. By the Central Limit Theorem, we have that:

`s = (1.5)/(√(83)) = 0.16`

The point estimate for the population standard deviation of the length of the walking canes is 0.16.