Question

1. Given a two-tailed test with test statistic a = 1.62 and n = 0.10, find the the p-value and determine if we reject or fail to reject ho. Say why

2. 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

1)

p value =2*P(z>1.62) = 0.1052

α=0.10

p value >α , do not reject Ho

2)

i)

Ho :   p =    0.56

ii)

H1 :   p ╪   0.56

iii) Level of Significance,   α =    0.05

iv)

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

v)

p-Value   =   0.0363   [excel formula =2*NORMSDIST(-z)]

vi)

Decision:   p-value<α , reject null hypothesis       

vii)

conclusion: There is enough evidence to reject the claim that Clairmont Elementary’s results the same as the state percentage