Hypothesis Tests Concerning Variance

[Fehling73]

Hi community,

How you all doin'?
Quick question on volume 1, example 7, page 617;
Identify the rejection point or points for the hypothesis tested in Part 1 at the 0.05 level of significance. The solution indicates to take df=23, under the 0.95 column …
Why not take the df=23, and 0.05 value? Thx.
Thank you for your effort and I look forward to hearing from you soon.

Best wishes,
Christoph

 

[Pieuwie]

Hi Christoph,
I Have been puzzeling as well why this is correct. But I think it is indeed correct.
They stated as H0: sigma squared greater than or equal to 16. This corresponds with the third null hypothesis. The rejection point of the third hypothesis is 1 minus alpha. This is due to the fact that the Chi-distribution is asymmetrical and bounded by 0.
This 1 minus alpha is stated at the rejection point of the first hypothesis, with the difference that this is a one-tailes test and therefore you should not divide alpha by 2 (see paragraph just above the example).
I hope this will help.
Kind regard,
Pieuwie

 

[jyk026]

if you look at the top of the chi squared table it asks for the probability, which is 95% (=1 - level of sig.), NOT the level of significance (5%). So it’d be a probability of 95 percent and df = n-1 which is 23 and a rejection point of 13.091.

 

[Fehling73]

Hi guys,
Thank you for your answers. The table was quite confusing as there was mentioned (Degrees of Freedom, Level of Significance) but under that “Probability of Right Tail, therefore, the 0.95 column.
Thanks again for your help.
TTYS
Best wishes,
Christoph