Question

14. A coin is flipped 100 times, and 59 heads are observed. Find a 80% confidence interval of π (the true population proportion of getting heads) and draw a conclusion based on the collected data.

Find the P-Value of the test. Ha: π =1/2. Vs. Ha: π ≠1/2.

A) Less than 1%.

B) Between 1% and 2%

C) Between 2% and 3%

D) Between 3% and 4%

E) Between 4% and 5%

F) Between 5% and 7%

G) Between 7% and 9%

H) Between 9% and 11%

I) Between 11% and 15%

J) Bigger than 15%.

Answer 1

a)

Level of Significance,   α =    0.20          
Number of Items of Interest,   x =   59          
Sample Size,   n =    100          
                  
Sample Proportion ,    p̂ = x/n =    0.5900          
z -value =   Zα/2 =    1.282   [excel formula =NORMSINV(α/2)]      
                  
Standard Error ,    SE = √[p̂(1-p̂)/n] =    0.049183          
margin of error , E = Z*SE =    1.282   *   0.04918   =   0.0630
                  
80%   Confidence Interval is              
Interval Lower Limit = p̂ - E =    0.59000   -   0.06303   =   0.52697
Interval Upper Limit = p̂ + E =   0.59000   +   0.06303   =   0.65303
                  
80%   confidence interval is (   0.527   < p <    0.653   )

b)

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

Number of Items of Interest,   x =   59                  
Sample Size,   n =    100                  
                          
Sample Proportion ,    p̂ = x/n =    0.5900                  
                          
Standard Error ,    SE = √( p(1-p)/n ) =    0.050                  
Z Test Statistic = ( p̂-p)/SE = (   0.5900   -   0.5   ) /   0.0500   =   1.8000
                          

                          
p-Value   =   0.0719   [excel formula =2*NORMSDIST(z)]              

G) Between 7% and 9%