Statistics hypothesis test question?
A study has a random sample of 20 subjects. The test
statistic for testing H0 : µ = 150 vs Ha : µ 6= 150 is t
=1.58. If the same sample mean and standard deviation
had been based on n =10 instead of n=20, the test
statistic would have been t =1.12. Would the P-value
for be larger, or smaller than when t =1.58?
A. Both p-values are same
B. p-value associated with 1.12 will be larger
C. p-value associated with 1.12 will be smaller
D. None of the above
I know the correct answer is B but I don't understand why.
- AlanLv 71 month ago
It is > test
Since you are in the end , you always want to compare to alpha
(significance level) in the end.
Sometimes people called p = 1 - actual p then you check for
Look at this table , it is for Row DF = 10
say alpha (significance level ) = 0.025
for t = 1.812 has
actual p = 0.95
for one tailed test, value tested against alpha
new p = 1- p = 0.05
so in table, sometimes the table just calls the the alpha value.
so it depends which value , you are calling p
so textbook will call p= 0.95 and other call p = 0.05
(so it can be compared directly to alpha.)
for t = 2.228 , for actual p = 0.975
value checked against alpha new p = 1-0.975 = 0.025
so if you are checking against the actual p value ,
larger T value has a larger p values.
if you are checking again what some textbooks call
p which is really 1-p , the larger T has a smaller P values.
so along the top row is the actual P value
the 2nd row is 1 - actual p sometimes labelled alpha in tables
for one -tailed test.
The 3rd row is 1 - actual p/2 used to two-sided test
The last row are the t-values.
Also, see the graph , so are you calling p the amount to the right of "t"
value or the area to the left of "t" value.