Question

A researcher is interested in estimating the savings account balance of customers at a large bank. She obtains the savings account balance of a random sample of 30 customers. A 95% confidence interval for the mean savings account balance of bank customers is found to be ($3402.08, $4142.75). Calculate a 95% confidence interval for the true mean length of the shafts.

Answer 1

Answer:

The 95% confidence interval for the true mean length of the shafts is ($3402.08, $4142.75).

Step-by-step explanation:

A (1 - α)% confidence interval for true mean (μ), when the population standard deviation is known is:

$CI=\bar x\pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

If the population standard deviation is not known, then the confidence interval for true mean is:

$CI=\bar x\pm t_{\alpha/2, (n-1)}\frac{s}{\sqrt{n}}$

A 95% confidence interval for true mean is an interval estimate of the population mean. The interval has 0.95 probability of consisting the true value of the population mean.

It is provided that the 95% confidence interval for mean, based on a sample of size 30 is ($3402.08, $4142.75).

This interval implies that the true mean value is between $3402.08 and $4142.75 with 95% confidence.

Thus, the 95% confidence interval for the true mean length of the shafts is ($3402.08, $4142.75).