Scenario 8.2 The undergraduate grade point average (GPA) for students admitted to the top graduate business...

Scenario 8.2

The undergraduate grade point average (GPA) for students admitted to the top graduate business schools was 3.37. Assume this estimate was based on a sample of 90 students admitted to the top schools. Using past years' data, the population standard deviation can be assumed known as 0.30.

1. Based on the information in Scenario 8.2, you are to construct a 95% confidence interval estimate of the mean undergraduate GPA for students admitted to the top graduate business schools, that is
[ Lower limit , Upper limit ].

The Lower limit of this 95% confidence interval is equal to ? (to 2 decimals)?

2. Based on the information in Scenario 8.2, you are to construct a 95% confidence interval estimate of the mean undergraduate GPA for students admitted to the top graduate business schools, that is
[ Lower limit , Upper limit ].

The Upper limit of this 95% confidence interval is equal to ? (to 2 decimals)?

Expert Solution

The formula for confidence interval estimation is:

μ = M ± Z(s_M)

where:

M = sample mean
Z = Z statistic determined by confidence level
s_M = standard error = √(s²/n)

M = 3.37
Z = 1.96
s_M = √(0.3²/90) = 0.03

μ = M ± Z(s_M)
μ = 3.37 ± 1.96*0.03
μ = 3.37 ± 0.062

95% CI [3.308, 3.432].

The lower limit is 3.31

2. The Upper limit is 3.43

Z table used for Z value calculation at 95% confidence level is

orchestra answered 1 year ago

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