# 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.

### 1 Answer

- AlanLv 78 months 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

p< alpha

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.