Question

A researcher has made ten attempts that are considered to be independent of each other where the probability of a successful attempt is p. Let X stand for the number of successful attempts. The researcher wants to try H0: P = 0.5 against H1: p> 0.5. The result of the ten trials was eight successful attempts. Calculate the p value.

The answer is p=0.0547

Show a good method to solve this question and write very big so i can read it.

Thank you :)

Answer 1

Ho :   p =    0.5
H1 :   p >   0.5

Number of Items of Interest,   x =   8
Sample Size,   n =    10
      
Sample Proportion ,    p̂ = x/n =    0.80
      
Standard Error ,    SE = √( p(1-p)/n ) =    0.1581
      
Z Test Statistic =    Z = ( p̂-p)/SE = (0.80-0.50)/0.1581 = 1.8974

p-Value   = P(Z>1.8974) = 0.0289 [Excel function =NORMSDIST(-z)

p-value will be 0.0289 (not 0.0547 , because it is a one tail test)