# Thread: P-value and Degrees of Freedom

1. ## P-value and Degrees of Freedom

Hello. For the question below I can get

2. It's a well-documented fact that the world over, 55% of the population prefers
Coke and 45% prefer Pepsi. Rumour had it that in Quebec, less than 55% of the
population prefers Coke, so an enterprising anthropologist went there to investigate.
He found, in a simple random sample, that 505 out of 1001 people preferred Coke.
Using these data, test the hypothesis that the proportion of people that prefer Coke
in Quebec is less than 0.55.

Null p=0.55
Alt p< 0.55

From the equation I got -2.89

and then my prof got the p-value.
p-value = 0.0019

I don't understand how he got the p-value.

Thank you!

2. Originally Posted by lou.loubunny
Hello. For the question below I can get

2. It's a well-documented fact that the world over, 55% of the population prefers
Coke and 45% prefer Pepsi. Rumour had it that in Quebec, less than 55% of the
population prefers Coke, so an enterprising anthropologist went there to investigate.
He found, in a simple random sample, that 505 out of 1001 people preferred Coke.
Using these data, test the hypothesis that the proportion of people that prefer Coke
in Quebec is less than 0.55.

Null p=0.55
Alt p< 0.55

From the equation I got -2.89

and then my prof got the p-value.
p-value = 0.0019

I don't understand how he got the p-value.

Thank you!
He looked a z-score of -2.89 up in a table of the cumulative standard normal distribution (or rather he looke up a z-score of 2.89 and subtracted the p-value of that from 1 (or 0.5 depending on the form of the table))

Here the normal distribution is appropriate as we are dealing with large sample statistics.

CB