A Professor hastaught statistics for 41 years and has kept the scores of everyte

Question

A Professor hastaught statistics for 41 years and has kept the scores of everytest he has ever given. Every test has been worth 100 points. He isinterested in the average test score over the years. Hedoesn’t want to put all of the scores (there are thousands ofthem) into a computer to figure out the exact average, so he askshis daughter to randomly select 50 of the tests and use those tocome up with an estimate of the population average. His daughterhas been studying statistics at college, decides to create a 98 %confidence interval for the true average test score. The mean testscore for the 50 random selected tests she selects is 73.5 with astandard deviation of 7.1. What does she tell herfather?  

Explanation / Answer

Looking at a standard z-score table, we can see that the way tofind a 98% confidence interval is to find everything within 2.33standard deviations of the mean. See here: Z-Score andConfidence Intervals 2.33*7.1 = 16.543 73.5 ± 16.543 = 98 percent confidence interval (56.96,90.04)

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