Question

1. In a random sample of 300 Las Cruces residents who drive a domestic car, 50 reported owning a hybrid car, whereas another sample of 350 El Pas residents who drive a domestic car revealed 30 who owned a hybrid car. Assume a = .05 a. Perform a hypothesis testing procedure to determine if the proportion of Las Cruces drivers that own a hybrid car is higher than the proportion in El Paso. b. Suppose p = 0.15 and p = 0.1 What is the sample size required to have a power of.95? C. Construct a 95% Cl and interpret this interval.

Answer 1

c.

Pooled proportion= p = (50+30)/(300+350) = 0.1231

p̂1 = 50/300 = 0.1667 , (1 - p̂1) = 0.8333 , p̂2 = 30/350 = 0.0857 , (1-p̂2) = 0.9143

n1 = 300 , n2 = 350

level of significance, α =   0.05              
Z critical value =   Z α/2 =    1.960   [excel function: =normsinv(α/2)      
                  
Std error , SE =    SQRT(p̂1 * (1 - p̂1)/n1 + p̂2 * (1-p̂2)/n2) = 0.0262
margin of error , E = Z*SE =    1.960   *   0.0262   =   0.05137
                  
confidence interval is                   
lower limit = (p̂1 - p̂2) - E =    0.081   -   0.0514   =   0.0296
upper limit = (p̂1 - p̂2) + E =    0.081   +   0.0514   =   0.1323
                  
so, confidence interval is (   0.0296   < p1 - p2 <   0.1323   )  

we are 95 confident that true difference of proportions lies within the confidence interval.

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