Question

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A survey of 430 randomly chosen adults found that 21% of the 222 men and 18% of the 208 women had purchased books online. A researcher used a Z Test Difference of Proportions to investigate this observed difference in proportions and calculated p-value 0.22.

a. Each of the following conclusions is wrong. Briefly explain why.

1. There is strong evidence that men are more likely than women to purchase books online.

2. There is a 22% chance that the same proportion of men and women buy books online.

3. Since the p-value is high, we have evidence that there is no difference in the proportions of men and women who buy books online.

b. Write a meaningful conclusion for this hypothesis test.

Answer 1

Ho:   p1 - p2 =   0          
Ha:   p1 - p2 >   0          
                  
sample #1   ----->              
first sample size,     n1=   222          
number of successes, sample 1 =     x1=   46.62          
proportion success of sample 1 , p̂1=   x1/n1=   0.2100          
                  
sample #2   ----->              
second sample size,     n2 =    208          
number of successes, sample 2 =     x2 =    37.44          
proportion success of sample 1 , p̂ 2=   x2/n2 =    0.1800          
                  
difference in sample proportions, p̂1 - p̂2 =     0.2100   -   0.1800   =   0.0300
                  
pooled proportion , p =   (x1+x2)/(n1+n2)=   0.195488372          
                  
std error ,SE =    =SQRT(p*(1-p)*(1/n1+ 1/n2)=   0.03827          
Z-statistic = (p̂1 - p̂2)/SE = (   0.030   /   0.0383   ) =   0.78
                  
p-value =        0.22 [excel function =NORMSDIST(-z)]      

Conclusion:   There is not enough evidence to conclude that men are more likely than women to purchase online.

There is strong evidence that men are more likely than women to purchase books online. Incorrect as opposite is true

There is a 22% chance that the same proportion of men and women buy books online. 22% chances are that men more likelt than women

Since the p-value is high, we have evidence that there is no difference in the proportions of men and women who buy books online. High p value might also indicate that women are more likely than men

b)

Conclusion:   There is not enough evidence to conclude that men are more likely than women to purchase online.

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