Question

The population standard deviation for the heights of dogs, in inches, in a city is 3.7 inches. If we want to be 95% confident that the sample mean is within 2 inches of the true population mean, what is the minimum sample size that can be taken? z0.101.282z0.051.645z0.0251.960z0.012.326z0.0052.576 Use the table above for the z-score, and be sure to round up to the nearest integer

Answer 1

Solution :

The minimum sample size needed to estimate the population mean with 95% confidence is given as follows :

Where, n is sample size, E is margin of error, σ is population standard deviation and Z(0.05/2) is critical z-value at 95% confidence level.

We want that sample mean is within 2 inches of the true population mean, therefore

Margin of error (E) = 2

σ = 3.7 inches

Using the Z-table we get, Z(0.05/2) = 1.96

Hence, required sample size is,

On rounding the value of n to the nearest integer we get,

n = 13

Hence, the minimum sample size that can be taken is 13.

Please rate the answer. Thank you.