Question

What are the conditions for using the standard deviation formula when conducting a significance test? Be specific about p versus p-hat.

Answer 1

@Jaylikescookies @bbbbbbbbbbbbbbbbbb

Answer 2

@Kayleedid @Jaydenthequiet

Answer 3

I don't know

Answer 4

How about this one?
In the 1996 regular baseball season, the World Series Champion New York Yankees played 80 games at home and 82 games away. They won 49 of their home games and 43 of the games played away. We can consider these games as samples from potentially large populations of games played at home and away.

a. Combining all of the games played, what proportion did the Yankees win?

b. Find the standard error needed for testing that the probability of winning is the same at home and away.

c. Most people think that it is easier to win at home than away. Formulate null and alternative hypotheses to examine this idea.

d. Compute the z statistic and its P-value. What conclusion do you draw?

Answer 5

That is not the question it just states that you need to be clear about which you are talking about.

Answer 6

@amistre64

Answer 7

which question?

Answer 8

Both eventually, but can we start with the first?

Answer 9

well, lets start by telling me what the standard deviation formula is, since we will need to assess it.

Answer 10

I am terrible at remembering formulas, thus I don't remember...

Answer 11

then question one is too vague for me to work with at the moment.

Answer 12

one formula is from start of it all such that sd = sqrt(var):\[Var(x)=\frac{\sum(x-\bar x)^2}{n-1}\]

Answer 13

another is:\[z=\frac{\hat p-p}{\sqrt{pq/n}}\]

Answer 14

Then how about the second question?

Answer 15

the second one ... part a is simple enough.

part b may be refering to a pooled sample data if memory serves

Answer 16

\[s_d\sqrt{\frac{p_aq_a}{n_a}+\frac{p_hq_h}{n_h}}\]
such that sd is teh standard deviation of ... something id have to google to be sure of at the moment

Answer 17

sp not sd ... sp is a weighted average of the standard deviations:\[s_p=\frac{(n_1-1)s_1^2+(n_2-1)s_2^2}{(n_1-1)+(n_2-1)}\]

Answer 18

ugh ... the sp part is only valid in cases where the standard deviations are assumed to be equal :/

Answer 19

the standard error just uses the formula:

\[SE=\sqrt{\frac{p_aq_a}{n_a}+\frac{p_hq_h}{n_h}}\]