Question

In a fourth year Engineering class at CSU Chico the average grade in the course which contained 23 fourth year students was 43.67 percentage points with a standard deviation of 7.53 percentage points. You are a second year Engineering student and you would like to establish a 95% confidence interval for the true average in this Engineering class that you too will have to take as a fourth year student.

Question 30:

Choose the appropriate interval from below for the 95% confidence interval for the true average in this fourth year Engineering class at CSU Chico.

Possible Answers:

a)    (40.974, 46.366)

b)    (40.593, 46.747)

c)    (40.414, 46.926)

d)    Can’t answer this question based on the information

e)    None of the above

Answer 1

sample mean, xbar = 43.67
sample standard deviation, s = 7.53
sample size, n = 23
degrees of freedom, df = n - 1 = 22

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 2.074

CI = (x-te x 18 +te x )

CI = (43.67 - 2.074 * 7.53/sqrt(23) , 43.67 + 2.074 * 7.53/sqrt(23))
CI = (40.414 , 46.926)