Question

Suppose that in a simple random sample of 100 people, 69 of them believe the Seahawks will win the Superbowl this year. We want to determine if the proportion of people in the population who believes this is less than 0.75.

Choose the appropriate concluding statement.

a. The sample data do not provide evidence that the proportion of people who believe the Seahawks will win the SuperBowl is less than 0.75.

b. The sample data provide evidence that the proportion of people who believe the Seahawks will win the SuperBowl is less than 0.75.

c. The sample data do not provide evidence that the proportion of people who believe the Seahawks will win the SuperBowl is less than 0.69.

d. The sample data provide evidence that the proportion of people who believe the Seahawks will win the SuperBowl is less than 0.69.

e. The sample data do not provide evidence that the proportion of people who believe the Seahawks will win the SuperBowl is greater than or equal to 0.75.

f. The sample data provide evidence that the proportion of people who believe the Seahawks will win the SuperBowl is greater than or equal to 0.75.

Answer 1

Null hypothesis     

               
                      
Alternative hypothesis          

           
                      
We have for given example,                      
Population proportion value is =0.75                  
x=69                  
                      
n=100                  
Level of significance =   0.05                  
Estimate for sample proportion =   
                      
Z test statistic formula for proportion


                      
=-1.39  
                      
              
P-value=   0.0829 ............................by using Z table or by using NORMSDIST(-1.39)

P value is 0.0829 >0.05   
Decision:   Do not reject H0              

a. The sample data do not provide evidence that the proportion of people who believe the Seahawks will win the SuperBowl is less than 0.75.