PDA

View Full Version : Question on decision rule

ajk003
03-02-2006, 09:53 PM
I'm a little confused on how to make a decision rule given an alpha value.
For example if the problem was a two ailed z test with a alpha of .03, what would I have to do to get the z value? Do I divide .03?

JohnM
03-02-2006, 09:55 PM
Yes, divide .03 by 2 to get .015. In a two-tailed test, the probability that you incorrectly reject Ho (alpha) needs to be split up between the two tails, because you can be wrong in either direction.

ajk003
03-03-2006, 01:01 PM
How would I find the probability of incorrectly rejecting the Ho? Would I have to look it up the z score chart? so for the problem above..the decision rule for a two tailed z test; alpha= .03 would be reject Ho at alpha= 0.03 if z is greater than or equal to 2.17???

JohnM
03-03-2006, 01:17 PM
It's the same as alpha.

When alpha is set to a particular value, this is the level of "risk" you are willing to take when rejecting Ho. A very low level of alpha, say .001, means that you are looking for a relatively large z score (positive or negative), which correlates with "a lot of evidence against Ho."

In other words, with alpha = .001 you want to be "really sure" or 99.9% sure (sure = "confidence level") that Ho is not true.

Yes, a z-score of 2.17 or -2.17 would be required to reject Ho with a two-tailed test and alpha set at .03.

With alpha set at .03, if you get a z-score outside of 2.17 or -2.17, then you can reject Ho with a 97% confidence level.
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "url": "http://www.talkstats.com/archive/index.php/t-628.html", "fetch_time": 1369203126000000000, "content_mime_type": "text/html", "warc_filename": "crawl-data/CC-MAIN-2013-20/segments/1368701409268/warc/CC-MAIN-20130516105009-00067-ip-10-60-113-184.ec2.internal.warc.gz", "warc_record_offset": 755728214, "warc_record_length": 2029, "token_count": 431, "char_count": 1508, "score": 3.5625, "int_score": 4, "crawl": "CC-MAIN-2013-20", "snapshot_type": "latest", "language": "en", "language_score": 0.9486031532287598, "file_path": "/sailhome/yjruan/project/latent-lm/data/processed/finemath-4plus/finemath-4plus/train-00032-of-00064.parquet"}