Hypothesis

Sue0113

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During the 2000 season, the home team won 138 of the 240 regular season National Football League games. Is this strong evidence of a home field advantage in professional football? Test an appropriate hypothesis and state your conclusion. Be sure the appropriate assumptions and conditions are satisfied before you proceed.
H°:p=0.5 HA:p>0.5Results of one game should not impact another, so games areindependent; data are all results for one season, which should be representativeof all seasons; Sample size is less than 10% of all games; (0.5)(24) >10 ; P-value = 0.0101. With a P-valuethis low, reject .. These data show strong evidence that thehome team does have an advantage; they win more than 50% of games at home.
Is there more to this question or is that it?
Am I working this question correctly?
 
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During the 2000 season, the home team won 138 of the 240 regular season National Football League games. Is this strong evidence of a home field advantage in professional football? Test an appropriate hypothesis and state your conclusion. Be sure the appropriate assumptions and conditions are satisfied before you proceed.
H°:p=0.5 HA:p>0.5
Results of one game should not impact another, so games are independent; data are all results for one season, which should be representative of all seasons;
Sample size is less than 10% of all games; <--- I don't know what this means, or if it is relevant
(0.5)(240) >10 ;
P-value = 0.0101.
<--- I don't know where this came from, or what test you are using
With a P-value this low, reject
..
These data show strong evidence that the home team does have an advantage; they win more than 50% of games at home.

Is there more to this question or is that it?
I want to know more about the distribution, and how you come up with a critical value. What is the meaning of P in H0 and in HA? I would call it p instead of P, and relate it to the Binomial Distribution. Then I want to see what are the mean and the standard deviation of the distribution .. you have shown that conditions allow the use of a Normal Distribution with the same mu and sigma.
mu = p*n = (0.5)(240) = 120
sigma = sqrt(n*p*(1-p)) = 7.75

What is your test statistic? Since I don't know anything better, I would use z = "the number of standard deviations away from the mean" as the test.

You have to choose a confidence value, like 95%. Find the critical value of z such that 95% of the normal distribution lies below z, or the tail is at most 5%. Then instead of saying "strong evidence," your statement would be "at the ... confidence level, the null hypothesis is rejected."

If you use any test more advanced than the simple normal distribution, you are going to have to tell me what it is.
 
All information is included

The question is stated as given to the class to solve.
The chapter we are working on is Testing Hypothesis about Proportions

 
The question is stated as given to the class to solve.
The chapter we are working on is Testing Hypothesis about Proportions
Have you followed a similar example from the book?

Does the book shed any light on the questions I asked, or is it completely different? Can you describe the method used in the book, in a few words?
 
In the book they talk about finding p-values but in all the examples it shows a percentage this question doesn't so I inserted 50% to solve it.
Example is for a two sided alternative I believe this question is a one sided alternative and I tried to solve as such.
Ho :p=0.50 HA :p >0.50
Results of one gameshould not impact another, so games are independent; data are all results forone season, which should be representative of all seasons; sample size is lessthan 10% of all games; (0.50)(240)> 10; Z=2.32; P-value = 0.0101
With a P-value this low; reject Ho. These data show strongevidence that the home team does have advantage; they win more than 50% ofgames at home.
The formula is for null model of a normal distribution.
This is the full Question, maybe I'm interpeting it incorrectly.
Duringthe 2000 season, the home team won 138 of the 240 regular season NationalFootball League games. Is this strong evidence of a home field advantage inprofessional football? Test an appropriate hypothesis and state yourconclusion. Be sure the appropriate assumptions and conditions are satisfiedbefore you proceed.

 
further information

I attached a file which explains what format we should be using to solve the question.
 

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In the book they talk about finding p-values but in all the examples it shows a percentage this question doesn't so I inserted 50% to solve it.
Example is for a two sided alternative I believe this question is a one sided alternative and I tried to solve as such. Yes, one sided.
Ho :p=0.50 HA :p >0.50
Results of one gameshould not impact another, so games are independent; data are all results forone season, which should be representative of all seasons; sample size is lessthan 10% of all games; (0.50)(240)> 10; Z=2.32; P-value = 0.0101
With a P-value this low; reject Ho. These data show strongevidence that the home team does have advantage; they win more than 50% ofgames at home.
The formula is for null model of a normal distribution.
This is the full Question, maybe I'm interpeting it incorrectly.
Duringthe 2000 season, the home team won 138 of the 240 regular season NationalFootball League games. Is this strong evidence of a home field advantage inprofessional football? Test an appropriate hypothesis and state yourconclusion. Be sure the appropriate assumptions and conditions are satisfiedbefore you proceed.
Thanks - that does clarify it for me a lot!
For instance, it is nice to know the null model is a normal distribution - and I got the same value of z that you did, z=2.32. But when I looked it up in the table, I looked up 2.23 instead of 2.32, so I got a different "P-value" than you did. That set me to wondering if we were using the same distribution. So now I agree with you fully!

I still don't know what they meant by "sample size is less than 10%," but it doesn't seem to matter.

[The more of your work we see, the more likely we are to understand.]
 
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