Question

2. A scientist averages several measurements to estimate the average depth of a river. He wants to be 90% confident that his estimate is accurate to within 0.4 foot. The population standard deviation of the depths measured is σ = 4.5 feet.

1. Find the number of measurements, n, to be included in the sample.

A 90% confidence requires ___________ measurements.

2. If the confidence level is changed to 99%, find the number of measurements, n, to be included in the sample.

A 99% confidence requires _________________measurements.

Answer 1

2)

Solution :

Given that,

Population standard deviation = = 4.5

Margin of error = E = 0.4

(a)

Z_/2 = 1.645

sample size = n = [Z_/2* / E] ²

n = [1.645 * 4.5 / 0.4]²

n = 343

A 90% confidence requires 343 measurements.

(b)

Z_/2 = 2.576

sample size = n = [Z_/2* / E] ²

n = [2.576 * 4.5 / 0.4]²

n = 840

A 90% confidence requires 840 measurements.