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28 August, 06:51

A chemist examines 14 sedimentary samples for magnesium concentration. The mean magnesium concentration for the sample data is 0.030 cc/cubic meter with a standard deviation of 0.0771. Determine the 90% confidence interval for the population mean magnesium 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.

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  1. 28 August, 07:01
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    Answer: ( - 0.007, 0.067)

    Step-by-step explanation: from the question, we are to construct a 90% confidence interval for mean magnesium concentration of a sample data.

    The parameters given to us are

    Sample mean (x) = 0.03

    Sample standard deviation (s) = 0.0771

    Sample size (n) = 14.

    The formulae for Constructing a 90% confidence interval for population mean is given below as

    u = x + tα/2 * (s/√n) ... For upper limit

    u = x - tα/2 * (s/√n) ... For lower limit.

    tα/2 = critical value for a t test at 10% level of significance.

    We are making use of a t critical value because our sample size is less than 30 (n = 14) and the population standard deviation is not given (so we were given the sample standard deviation, s = 0.0771)

    The value of tα/2 is gotten using a t distribution table by checking the level of significance (10%) against the degree of freedom (df = n - 1 = 14 - 1 = 13).

    From the table, we have tα/2 as 1.771

    For upper tailed

    u = 0.03 + 1.771 * (0.0771/√14)

    u = 0.03 + 1.771 (0.0206)

    u = 0.03 + 0.0365

    u = 0.067

    For lower tailed

    u = 0.03 - 1.771 * (0.0771/√14)

    u = 0.03 - 1.771 (0.0206)

    u = 0.03 - 0.0365

    u = - 0.007

    Hence the 90% confidence interval for mean magnesium concentration is given as ( - 0.007 cc/cubic meter, 0.067 cc/cubic meter)
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