A sample of 81 calculus students at a large college had a mean mathematics ACT score of 26 with a standard deviation of 6. Find a 95% confidence interval for the mean mathematics ACT score for all calculus students at this college.
Accepted Solution
A:
Answer: 24.67 ≤ μ ≤ 27.33Step-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 nDegrees of freedom, df = n - 1 = 81 - 1 = 80 ∝ = 100 - 95 = 5% = 0.05 thus ∝/2 = 0.025From the t distribution t (0.025,80) = 1.990Substituting into the formula:26 - 1.990 x 6/sqrt 81 ≤ μ ≤ 26 + 1.990 x 6/sqrt 8124.67 ≤ μ ≤ 27.33