In: Statistics and Probability
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?
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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