Consider the following hypotheses Which of the following sam

Consider the following hypotheses:

Which of the following sample information enables us to reject the null hypothesis at = 0.01 and at
= 0.10? Use Table 1.

Solution

a)

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   >=   0.45
Ha:   p   <   0.45
As we see, the hypothesized po =   0.45      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.330275229      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.047651256      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    -2.512520773      
          
As this is a    1   tailed test, then, getting the p value,  
          
p =    0.005993602      

Thus, we REJECT BOTH AT 0.01 AND 0.10. [ANSWER]

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b)

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   >=   0.45
Ha:   p   <   0.45
As we see, the hypothesized po =   0.45      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.339222615      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.029572932      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    -3.745904713      
          
As this is a    1   tailed test, then, getting the p value,  
          
p =    8.98724E-05      

Thus, we REJECT BOTH AT 0.01 AND 0.10. [ANSWER]

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c)

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   >=   0.45
Ha:   p   <   0.45
As we see, the hypothesized po =   0.45      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.39      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.066480395      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    -0.90252172      
          
As this is a    1   tailed test, then, getting the p value,  
          
p =    0.183389894      

Thus, we DO NOT REJECT FOR BOTH 0.01 AND 0.10.

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d)

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   >=   0.45
Ha:   p   <   0.45
As we see, the hypothesized po =   0.45      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.39      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.024333213      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    -2.465765601      
          
As this is a    1   tailed test, then, getting the p value,  
          
p =    0.006836039      

Thus, we REJECT BOTH AT 0.01 AND 0.10. [ANSWER]