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2 August, 04:57

A geologist examines 6 seawater samples for lead concentration. The mean lead concentration for the sample data is 0.903 cc/cubic meter with a standard deviation of 0.0566. Determine the 95% confidence interval for the population mean lead concentration. Assume the population is approximately normal.

Step 2 of 2:

Construct the 95% confidence interval. Round your answer to three decimal places.

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  1. 2 August, 07:33
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    Step-by-step explanation:

    We want to determine a 95% confidence interval for the mean lead concentration of sea water samples

    Number of samples. n = 6

    Mean, u = 0.903 cc/cubic meter

    Standard deviation, s = 0.0566

    For a confidence level of 95%, the corresponding z value is 1.96. This is determined from the normal distribution table.

    We will apply the formula

    Confidence interval

    = mean + / - z * standard deviation/√n

    It becomes

    0.903 + / - 1.96 * 0.0566/√6

    = 0.903 + / - 1.96 * 0.0566/2.44948974278

    = 0.903 + / - 0.045

    The lower end of the confidence interval is 0.903 - 0.045 = 0.858

    The upper end of the confidence interval is 0.903 + 0.045 = 0.948

    Therefore, with 95% confidence interval, the mean lead concentration of the sea water is between 0.858 cc/cubic meter and 0.948 cc/cubic meter
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