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

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?

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.

... H0: µ1 -µ2 greater than or equal to 0 versus H1: µ1 ... for mean not equal to 25,000 it would have been a two tailed test. ... d. a one-tailed test must be utilized. ...

... perform each kind of test (one versus two ... difference between two population proportions: Two-tailed test Lower Tail One-Tailed Test Upper Tail One-Tailed Test. ...

... Is your test one-tailed or two-tailed? ... can you say about your sample mean versus the population ... This is a two--tailed hypothesis test because my alternative "Ha ...

... brand of bulb is 750 hours versus the alternative that ... has the ≠ symbol in it, the test is two tailed. ... symbol in it, the test is one tailed (lower). ...

...2. Researcher conducts a one tailed two sample t test ... the difference in number of large versus small posters ... 1. A researcher conducts a two tailed two sample t ...

... advantage of using as alpha level of .01 versus a level ... In each case, use a two-tailed test with alpha (a ... Use a one-tailed test at the .05 level of significance ...

... all incoming circuits, so when each shipment arrives, a sample is then used to test H0: p = 0.05 versus HA: p ...2. Explain a one-tailed and two-tailed test. ...

... 20) Suppose we wish to test the null hypothesis H0: μ ≤ 47 versus H1: μ > 47. ... a one-tailed test. a two-tailed test. None of the above. ...