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One-Tailed vs. Two-Tailed & Type I and Type II Error

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1. The SEM for a particular intelligence test (mean of 100, standard deviation of 15) is 3 points. Ken Garoo obtains an IQ score of 126, but needs an IQ of 130 to qualify for a Talented and Gifted (TAG) class. Calculate the range of Ken's true score: (a) with 68% probability, and (b) with 95% probability. Should Ken be admitted into the TAG class?

2. Explain the advantages of a one-tailed verses a two-tailed test. If one-tailed tests are more powerful, then why bother with two-tailed tests at all?

3. Explain why there is an inverse relationship between committing a Type I error and committing a Type II error. What is the best way to reduce both kinds of error?

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Solution Preview

Please see the attachment for the missing part of the answers which are math-based.

1. a) Now, for the first part it is important to notice that a 68% percent probability is approximately equal to 1 standard deviation on either side of the mean. This means that the range of scores for 68% probability is calculated by: (see attachment for equation and mathematical steps).

1. b) It is also important to notice for this part of the problem that a 95% confidence interval is approximately equal to 2 standard deviations on either side of the mean. This means that the range of scores for 95% probability is ...

Solution Summary

This solution explains the different test types and errors in 434 words. The full formatted math-based discussion is provided in the attached Excel file.