Question

A physicist examines 4 water samples for mercury concentration. The mean mercury concentration for the sample data is 0.470 cc/cubic meter with a standard deviation of 0.0581. Determine the 80% confidence interval for the population mean mercury concentration. Assume the population is approximately normal. Step 1 of 2: Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Answer 1

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

We want to determine a 80% confidence interval for the mean mercury concentration of water samples

Number of samples. n = 4

Mean or average = 0.470 cc/cubic meter

Standard deviation, s = 0.0581

For a confidence level of 80%, the corresponding z value is 1.28. This is determined from the normal distribution table.

We will apply the formula

Confidence interval

= mean +/- z ×standard deviation/√n

It becomes

0.470 +/- 1.28 × 0.0581/√4

= 0.470 +/- 1.28 × 0.0566/2

= 0.470 +/- 0.036

The lower end of the confidence interval is 0.470 - 0.036 =0.434

The upper end of the confidence interval is 0.470 + 0.036 =0.506

In conclusion, with a 80% confidence interval, the mean lead mean mercury concentration of the water samples is between 0.434 cc/cubic meter and 0.506 cc/cubic meter