Question

Random samples of employees in fast-food restaurants where the employer provides a training program were drawn. Of a sample of 67 employees who had not completed high school, 11 had participated in a training program provided by their current employer. Of an independent random sample of 113 employees who had completed high school but had not attended college, 27 had participated. Test at the 1% significance level the null hypothesis that the participation rates are the same for the two groups against the alternative that the rate is lower for those who have not completed high school.

Conduct the appropriate hypothesis test and report the p-value. Do not round intermediate calculations. Round your answer to four decimal places. Include the leading zero. Format: 0.0000

Answer 1

Hypothesis Test: Difference of two Proportions              

Ho:   p1 - p2 =   0          
Ha:   p1 - p2 <   0          
                  
sample #1   ----->   not completed          
first sample size,                                     n1=   67          
number of successes, sample 1 =       x1=   11          
proportion success of sample 1 , p̂1=   x1/n1=   0.1642          
                  
sample #2   ----->   completed          
second sample size,                                     n2 =    113          
number of successes, sample 2 =       x2 =    27          
proportion success of sample 1 , p̂ 2=   x2/n2   =    0.2389          
                  
difference in sample proportions, p̂1 - p̂2 =     0.1642   -   0.2389   =   -0.0748
                  
pooled proportion , p =   (x1+x2)/(n1+n2)=   0.2111          
                  
std error ,SE =    =SQRT(p*(1-p)*(1/n1+ 1/n2)=   0.0629          
Z-statistic = (p̂1 - p̂2)/SE = (   -0.075   /   0.0629   ) =   -1.1881
                  

p-value =        0.1174                                     [Excel function =NORMSDIST(z)      
decision :    p-value>α,Don't reject null hypothesis