After losing a football game Tom conducted a survey to see i

After losing a football game, Tom conducted a survey to see if alumni were in favor of firing the coach. A simple random sample of 100 alumni was taken. 65 of the alumni in the sample were in favor of firing the coach. Suppose Tom wished to see if the majority of the alumni are in favor of firing the coach so he tests the hypotheses. What is the decision about claim?

A. There is sufficient evidence to reject the claim

B. There is not sufficient evidence to reject the claim

C. The sample data support the claim

D. There is not sufficient evidence to support the claim

E. None of the above

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      
          
As this is a    1   tailed test, then, getting the p value,  
          
p =    0.001349898      

As this is a small P value, we   REJECT THE NULL HYPOTHESIS. Hence, the proportion is significantly higher than 50%.

Thus,

OPTION C. The sample data support the claim. [ANSWER, C]