Question

In a recent survey of parents at Clairmont Elementary, 51 out of 75 parents supported including sign language as a part of the elementary school curriculum. In a survey of Minnesota elementary schools, it was published that 56% of parents support including sign language in elementary school curriculum. At a 5% level of significance, are Clairmont Elementary’s results the same as the state percentage? Conduct a seven-step hypothesis test.

Answer 1

Ho :   p =    0.56                  
H1 :   p ╪   0.56       (Two tail test)          
                          
Level of Significance,   α =    0.05                  
Number of Items of Interest,   x =   51                  
Sample Size,   n =    75                  
                          
Sample Proportion ,    p̂ = x/n =    0.6800                  
                          
Standard Error ,    SE = √( p(1-p)/n ) =    0.0573                  
Z Test Statistic = ( p̂-p)/SE = (   0.6800   -   0.56   ) /   0.0573   =   2.0936
                          
  
p-Value   =   0.0363   [excel formula =2*NORMSDIST(z)]              
Decision:   p-value<α , reject null hypothesis                       
There is enough evidence to reject the claim that 56% of parents support including sign language in elementary school curriculum