Consider that the annual precipitation values (in mm) in the district of Beja are normally distributed. It is intended to test if the average annual precipitation is greater than 500. For this, a sample of 20 years was collected, observing the following values: 607.4 345.4 497.6 464.0 809.1 620.0 728.1 809.1 488.8 407.7 602.3 721.8 481.1 513.3 672.0 533.9 592.8 527.4 581.1 384.2 Regarding the values in the table above, it is known that the sample mean is 569,355 mm and that s = 131.1834.
Consider the hypotheses H0: σ ≥ 130 vs H1: σ <130.
Assuming we collected another sample of dimension 20 for which the observed value of the test statistic is 11.651, then we can reject hypothesis H0 for any level of significance greater than 5%. The solution says that this sentence is false.
My doubt is: why is this false?
I tried with alfa=0.05 and since x^2 19,0.95 = 10.1 i didn't reject it
I tried alfa = 0.1 and got x^2 19,0.9 = 11.7 and since T=11.651 i reject it.
And with alfa = 0.2 the same thing
So i guess is right
Could someone help me please?