Question

A physicist examines 28 sedimentary samples for nitrate concentration. The mean nitrate concentration for the sample data is 0.443 cc/cubic meter with a standard deviation of 0.0305. Determine the 95% confidence interval for the population mean nitrate 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: 95% confidence interval is (0.432, 0.454) and critical value = 1.96.

Step-by-step explanation:

Since we have given that

Sample size = n = 28

Mean = 0.443

Standard deviation = 0.0305

We need to find the 95% confidence interval.

So, z = 1.96

so, Interval would be

$\bar{x}\pm z\dfrac{\sigma}{\sqrt{n}}\\\\=0.443\pm 1.96\times \dfrac{0.0305}{\sqrt{28}}\\\\=0.443\pm 0.0112\\\\=(0.443-0.0112,0.443+0.0112)\\\\=(0.4318,0.4542)\\\\=(0.432,0.454)$

Hence, 95% confidence interval is (0.432, 0.454) and critical value = 1.96.