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)