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.

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)