Question

During the 2007-2008 school year, approximately p = 0.64 of principals in Florida public schools were female. In a 2008-2009 school year survey, x = 231 of n = 328 randomly selected principals (estimated N = 2,121,000) in Florida public schools were female or ?̂ = 0.704. Conduct the appropriate hypothesis test to determine if there is sufficient evidence to conclude that the proportion of female principals in Florida public schools has changed. Use α = 0.05
a. Step 1: Verify the assumptions for the Distribution of the Sample Proportion ?̂ (3 pts)
• Sample is random
• Distribution is normally distributed, if n?0(1- ?0) ≥ 10
• n ≤ 0.05 of N
b. Step 2: State the null and alternative hypotheses (1 pt.):
c. Step 3: Determine the level of significance, α (1 pt.):
d. Step 4a: Calculate the test statistic (2 pts):
?0= ? ̂ − ?0√?0(1−?0)?
e. Step 4b: Determine the p-value of the test statistic (1 pt.):
f. Step 5: Compare the p-value of the test statistic to the alpha level, and decide whether to reject or retain Ho (1 pt.):
g. Step 6: State the conclusion of the hypothesis test in a full sentence (1 pt.):

Answer 1

a)

• Sample is random
• Distribution is normally distributed, if n?0(1- ?0) ≥ 10
• n ≤ 0.05 of N

b)

Ho :   p =    0.64  
H1 :   p ╪   0.64  

c)

Level of Significance,   α =    0.05

d)

Sample Proportion ,    p̂ = x/n =    0.704   
                          
Standard Error ,    SE = √( p(1-p)/n ) =    0.0265                  
Z Test Statistic = ( p̂-p)/SE = (   0.704 -   0.64   ) /   0.0265   =   2.4249

e)

p-Value   =   0.0153   [excel formula =2*NORMSDIST(z)]  

f)

Decision:   p-value<α , reject null hypothesis   

g)

There is enough evidence to conclude that  proportion of female principals in Florida public schools has changed