a true false test has 100 questions a passing grade is 65 or

a true false test has 100 questions   a passing grade is 65 or more correct answers   test claims that students knows more than half of the answers and is not just guessing   with a significance level of .05

what is z value?

what is p-value ?

recject null?

do not reject null?

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 =    0.65      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.05      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    3   [ANSWER, Z VALUE]

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As this is a right tailed test, then, getting the p value  
          
p =    0.001349898   [ANSWER, P VALUE]

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significance level =    0.05      

Comparing p < 0.05, we   REJECT THE NULL HYPOTHESIS.   [ANSWER]