Question

In: Statistics and Probability

An apparel company is running a market research in Vancouver and Toronto, about popularity of their...

An apparel company is running a market research in Vancouver and Toronto, about popularity of their sneakers among the teenagers. By sampling, it turned out that from 400 Vancouver teenage customers, 72 of them bought the sneakers, while from 500 Toronto teenage customers, 70 customers bought the product. With 6% significance level, can you conclude that the sneakers are more popular among Vancouver teenagers? Why?

Solutions

Expert Solution

Ho:   p1 - p2 =   0          
Ha:   p1 - p2 >   0          
                  
sample #1   ----->              
first sample size,     n1=   400          
number of successes, sample 1 =     x1=   72          
proportion success of sample 1 , p̂1=   x1/n1=   0.1800          
                  
sample #2   ----->              
second sample size,     n2 =    500          
number of successes, sample 2 =     x2 =    70          
proportion success of sample 1 , p̂ 2=   x2/n2 =    0.1400          
                  
difference in sample proportions, p̂1 - p̂2 =     0.1800   -   0.1400   =   0.0400
                  
pooled proportion , p =   (x1+x2)/(n1+n2)=   0.157777778          
                  
std error ,SE =    =SQRT(p*(1-p)*(1/n1+ 1/n2)=   0.02445          
Z-statistic = (p̂1 - p̂2)/SE = (   0.040   /   0.0245   ) =   1.64
                        
p-value =        0.0509   [excel function =NORMSDIST(-z)]      
decision :    p-value<α,Reject null hypothesis               
                  
Conclusion:   There is enough evidence to  
conclude that the sneakers are more popular among Vancouver teenagers

........

Please let me know in case of any doubt.

Thanks in advance!


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