Question

A physicist examines 4 seawater samples for potassium chloride concentration. The mean potassium chloride concentration for the sample data is 0.604 cc/cubic meter with a standard deviation of 0.0177. Determine the 80% confidence interval for the population mean potassium chloride concentration. Assume the population is approximately normal.

1)Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

2)Construct the 80% confidence interval. Round your answer to three decimal places.

Answer 1

Solution :

Given that,

= 0.604

s = 0.0177

n = 4

Degrees of freedom = df = n - 1 = 4 - 1 = 3

At 80% confidence level the t is ,

= 1 - 80% = 1 - 0.80= 0.20

/ 2 = 0.20 / 2 = 0.10

1) Critical value = t _/2,df = t_0.10,3 = 1.638

2) Margin of error = E = t_/2,df * (s /n)

= 1.638 * (0.0177 / 4)

= 0.014

The 80% confidence interval estimate of the population mean is,

- E < < + E

0.604 - 0.014 < < 0.604 + 0.014

0.590 < < 0.618

(0.590 , 0.618)