test the hypothesis using pvalue approach be sure to verify

Solution

a)

Here, po = 0.7, n = 200, then

n po (1 - po) = 200*0.7*(1-0.7) = 42 >= 10. [YES]

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b)

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   <=   0.7
Ha:   p   >   0.7
As we see, the hypothesized po =   0.7      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.725      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.032403703      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    0.77151675      
          
As this is a    1   tailed test, then, getting the p value,  
          
p =    0.220200349   [ANSWER, P VALUE]

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c)
  
significance level =    0.01      

FAIL TO REJECT the null hypothesis, because the P value is GREATER THAN alpha. [ANSWER]