Question

A random sample of n = 1,400 observations from a binomial population produced x = 659.

(a) If your research hypothesis is that p differs from 0.5, what hypotheses should you test?

H₀: p ≠ 0.5 versus H_a: p = 0.5H₀: p = 0.5 versus H_a: p < 0.5     H₀: p = 0.5 versus H_a: p > 0.5H₀: p < 0.5 versus H_a: p > 0.5H₀: p = 0.5 versus H_a: p ≠ 0.5

(b) Calculate the test statistic and its p-value. (Round your test statistic to two decimal places and your p-value to four decimal places.)

z	=
p-value	=

Answer 1

a)

H₀: p = 0.5 versus H_a: p ≠ 0.5

b)

We have for given example,                  
Population proportion value is =0.5              
x=659              
                  
n=1400              
          
Estimate for sample proportion =0.4707              
                  
Z test statistic formula for proportion                  


=-2.19  

P value = 0.0285...............by using Z table or by using Excel command =2*NORMSDIST(-2.19)