# 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

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.

Relevance
• 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. 