Hypothesis Testing Onesample test A questionnaire was sent

Hypothesis Testing – One-sample test

A questionnaire was sent to a large number of students, asking for their opinions about a proposal to alter an examination syllabus. Of the 180 replies, 134 were in favour of the proposal. Test, at 1% level, whether significantly more than 70% of all students were in favour of the proposal. State the necessary conditions to be met to conduct this hypothesis test.   

Solution

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 =    0.744444444      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.034156503      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    1.301200097      
          
As this is a    1   tailed test, then, getting the p value,  
          
p =    0.096594986      
significance level =    0.01      
Comparing p and the significance value, we   FAIL TO REJECT THE NULL HYPOTHESIS.      

Thus, there is no significant evidence that significantly more than 70% of all students were in favour of the proposal. [CONCLUSION]

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We assumed that each response are independent to each other, and that the sample size is sufficiently large (180), and the number of successes and failures are large enough (134 and 46). All these are satisfied.