Question

In a simple random of 400 of Deadpool fights, Deadpool breaks the Fourth Wall in 223 of them.

Colossus claims that Deadpool breaks the Fourth Wall in half of his fights. Do we have evidence that he's mistaken at each of the following levels?
The associated p-value for this hypothesis test is ( )? (Answers to four places after the decimal.)

(a) At the 20% level (Yes or No?)

(b)At the 13% level (Yes or No?)

(c)At the 10% level (Yes or No?)

(d)At the 7% level (Yes or No?)

(e)At the 5% level (Yes or No?)

(f)At the 3% level (Yes or No?)

(g)At the 2% level (Yes or No?)

(h)At the 1% level (Yes or No?)

(i) At the 0.2% level (Yes or No?)

(j) At the 0.1% level (Yes or No?)

Thank you very much! I will UPVOTE this answer!

Answer 1

Ho :   p =    0.5                  
H1 :   p ╪   0.5       (Two tail test)          
                          

Number of Items of Interest,   x =   223                  
Sample Size,   n =    400                  
                          
Sample Proportion ,    p̂ = x/n =    0.5575                  
                          
Standard Error ,    SE = √( p(1-p)/n ) =    0.0250                  
Z Test Statistic = ( p̂-p)/SE = (   0.5575   -   0.5   ) /   0.0250   =   2.3000

p-Value   =   0.0214   [excel formula =2*NORMSDIST(z)]              

(a) At the 20% level (YES )

(b)At the 13% level (YES)

(c)At the 10% level (YES)

(d)At the 7% level (YES)

(e)At the 5% level (YES)

(f)At the 3% level (YES)

(g)At the 2% level (NO)

(h)At the 1% level (NO)

(i) At the 0.2% level (NO)

(j) At the 0.1% level (NO)