You want to estimate the average GMAT score for all students who took the Logitano GMAT Preparation course during the past 2 years.You select a random sample of 100 such students from a comprehensive list of all students who took the course over the last two years and find that the average GMAT score for the sample was 1040.Assume you know the population standard deviation here is 83 points.Produce the 95% confidence interval estimate of the mean GMAT score for the population of Logitano students represented by the sample.Report the upper bound for your interval.
A)1234.1
B)1152.3
C)802.8
D)1056.3
E)1352.7

Question

Quizplus · Accepted Answer

The upper bound of the 95% confidence interval can be calculated using the formula: $ \bar{x} + Z \frac{\sigma}{\sqrt{n}} $, where $ \bar{x} $ is the sample mean, $ Z $ is the Z-score corresponding to the confidence level (for 95%, $ Z = 1.96 $), $ \sigma $ is the population standard deviation, and $ n $ is the sample size. Plugging in the given values: $ 1040 + 1.96 \frac{83}{\sqrt{100}} = 1040 + 1.96 \times 8.3 = 1040 + 16.3 = 1056.3 $.

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