A hypothesis test given by H0 p 05 H1 p 05 Ha p

A hypothesis test given by : H0 :p = 0.5, H1 :p = <0.5. In a random sample of 100 subjects, the sample proportion is found to be p^ = 0.47. Determine the test statistic and the p value.

Solution

POPULATION PROPORTION Z TEST GIVEN P^          
          
Formulating the null and alternatuve hypotheses,          
          
Ho:   p   >=   0.5
Ha:   p   <   0.5
As we see, the hypothesized po =   0.5      
As it is given,          
          
po =    0.5      
          
Getting the standard error of po, spo,          
          
spo = sqrt[po (1 - po) / n] =    0.05      
          
Getting the z statistic,          
p^ =    0.47      

z = (p^ - po)/spo =    -0.6   [ANSWER, TEST STATISTIC]

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As this is a    1   tailed test, then, getting the p value,  
          
p =    0.274253118 [ANSWER, P VALUE]