Answer:
P-value for this hypothesis test is 0.00175.
Step-by-step explanation:
We are given that 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.
<u><em>Let p = proportion of all living alumni who favored firing the coach</em></u>
SO, Null Hypothesis,  : p = 0.50   {means that the majority of alumni are not in favor of firing the coach}
 : p = 0.50   {means that the majority of alumni are not in favor of firing the coach}
Alternate Hypothesis,  : p > 0.50   {means that the majority of alumni are in favor of firing the coach}
 : p > 0.50   {means that the majority of alumni are in favor of firing the coach}
The test statistics that will be used here is <u>One-sample z proportion</u> <u>statistics</u>;
                                   T.S.  =  ~ N(0,1)
  ~ N(0,1)
where,  = sample proportion of the alumni in the sample who were in favor of firing the coach =
  = sample proportion of the alumni in the sample who were in favor of firing the coach =  = 0.64
 = 0.64
             n = sample of alumni = 100
So, <em><u>test statistics</u></em>  =  
                                =  2.92
<u>Now, P-value of the hypothesis test is given by ;</u>
          P-value = P(Z > 2.92) = 1 - P(Z  2.92)
 2.92) 
                                              = 1 - 0.99825 = 0.00175
Therefore, the P-value for this hypothesis test is 0.00175.