Question

The undergraduate grade point (GPA) for students admitted to the top graduate business shools was 3.37 assume this estimate was based on a sample of 120 students admited to the top schools, using past year data the population standard deviation can be assumed known with standard deviation = .28 what is the 95% confidence interval estimate of the mean undergraduate GPA for students admited to the top graduate business school?

Answer 1

We can use the formula:

( X̄ - z*(σ/√n), X̄ + z*(σ/√n) )

where:

X̄ = sample mean = 3.37
z = z-score for desired confidence level = 1.96 (from a standard normal distribution)
σ = population standard deviation = 0.28
n = sample size = 120

Plugging in the values, we get:

( 3.37 - 1.96*(0.28/√120), 3.37 + 1.96*(0.28/√120) )

Simplifying, we get:

( 3.28, 3.46 )

Therefore, we are 95% confident that the true mean undergraduate GPA for students admitted to the top graduate business schools is between 3.28 and 3.46.