Question

Below is an exercise sample out of my text book and when looking at the answer supplied, I do not understand how they are getting the p value using the t table. They say t = 2.02 is .0173. Can someone work this out and show me how they are getting the answer?

The Coca-Cola Company reported that the mean per capita annual sales of its beverages in the United States was 423 eight-ounce servings (Coca-Cola Company website, February 3, 2009). Suppose you are curious whether the consumption of Coca-Cola beverages is higher in Atlanta, Georgia, the location of Coca-Cola’s corporate headquarters. A sample of 36 individuals from the Atlanta area showed a sample mean annual consumption of 460.4 eight-ounce servings with a standard deviation of s = 101.9. Using a =.05, do the sample results support the conclusion that mean annual consumption of Coca-Cola beverage products is higher in Atlanta?

Answer 1

To Test -

H0 :-  

H1 :-

Test Statistic :-
t = ( X̅ - µ ) / (S / √(n) )
t = ( 460.4 - 423 ) / ( 101.9 / √(36) )
t = 2.02

Test Criteria :-
Reject null hypothesis if t > t(α, n-1)
t(α, n-1) = t(0.05 , 36-1) = 1.69
t > t(α, n-1) = 2.2022 > 1.69
Result :- Reject null hypothesis

Decision based on P value

Using excel we get the exact P value
P - value = P ( t > 2.02 ) = 0.0173
Reject null hypothesis if P value < α = 0.05 level of significance
P - value = 0.0172 < 0.05 ,hence we reject null hypothesis
Conclusion :- Reject null hypothesis

P value can be find in t table, looking for the t value t = 2.02 across n - 1 = 36 - 1 degree of freedom.