Question

After a college football team once again lost a game to their archrival, the alumni association conducted a survey to see if alumni were in favor of firing the coach. A simple random sample of 100 alumni from the population of all living alumni was taken. Sixty-four of the alumni in the sample were in favor of firing the coach. Let p represent the proportion of all living alumni who favored firing the coach. Suppose the alumni association wished to see if the majority of alumni are in favor of firing the coach. To do this they test the hypotheses H0: p = 0.50 versus Ha: p > 0.50. What is the P-value for this hypothesis test?

Answer 1

We have for given example,              
Population proportion value is =0.5          
x=64          
              
n=100          
Level of significance =   0.05          
Estimate for sample proportion = 0.64          
              
Z test statistic formula for proportion

  
One-Tailed test (Upper)              
      
P-value=   0.0026 ................................by using Excel command =1-NORMSDIST(2.8) or by using Z table.   
Decision=   Reject   H0