In a dietary study 14 of 20 subjects lost weight If weight i

In a dietary study, 14 of 20 subjects lost weight. If weight is assumed to fluctuate by chance, with probability 1/2 of losing weight, what is the exact two-sided p-value for testing the null hypothesis = 1/2?

Solution

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   =   0.5
Ha:   p   =/=   0.5
As we see, the hypothesized po =   0.5      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.7      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.111803399      
          
Getting the t statistic,          
          
t = (p^ - po)/sp =    1.788854382      
          
As this is a    2   tailed test, then, getting the p value, with df = 20 - 1 = 19,
          
p =    0.089595249   [ANSWER]