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

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  • Alan
    Lv 7
    1 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 

    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. 

    Attachment image
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