A student examines 27 geological samples for nitrate concentration. The mean nitrate concentration for the sample data is 0.819 cc/cubic meter with a standard deviation of 0.0881. Determine the 90% confidence interval for the population mean lead 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. Construct the 90% confidence interval. Round your answer to three decimal places

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JeanaShupp JeanaShupp · Answer 1 · 2019-10-24T07:48:27+02:00

Answer: 90% confidence interval: (0.790, 0.848)

Critical t- value for 90% confidence = 1.706

Step-by-step explanation:

As we consider the given description, we hvae

n= 27

[tex]\overline{x}=0.819[/tex]

s=0.0881

Since population standard deviation is unknown.

so we use t-critical value

Using t-value table , the critical t- value will be:-

[tex]t_{n-1,\ \alpha/2}=t_{26,\ 0.05}= 1.706[/tex]

Confidence interval : [tex]\overline{x}\pm t_{n-1,\alpha/2}\dfrac{s}{\sqrt{n}}[/tex]

i.e. [tex]0.819\pm ( 1.706)\dfrac{0.0881}{\sqrt{27}}[/tex]

[tex]\approx0.819\pm 0.029=(0.819-0.029,\ 0.819+0.029)\\\\=(0.790,\ 0.848)[/tex]

Hence, 90% confidence interval: (0.790, 0.848)