Answer: 24.67 ≤ μ ≤ 27.33
Step-by-step explanation:
From the information given: n = 81 students, Sample mean (x bar) = 26 and sample standard deviation (s) = 6.
Since the population standard deviation in unknown we use the student t distribution to estimate the mean. The mean is estimated as follows:
X bar - t (∝/2, n-1) x s/sqrt n ≤ μ ≤ X bar + t (∝/2, n-1) x s/sqrt n
Degrees of freedom, df = n - 1 = 81 - 1 = 80
∝ = 100 - 95 = 5% = 0.05 thus ∝/2 = 0.025
From the t distribution t (0.025,80) = 1.990
Substituting into the formula:
26 - 1.990 x 6/sqrt 81 ≤ μ ≤ 26 + 1.990 x 6/sqrt 81
24.67 ≤ μ ≤ 27.33
