Question

Conduct a test at the alphaequals0.01 level of significance by determining ​(a) the null and alternative​ hypotheses, ​(b) the test​ statistic, and​ (c) the​ P-value. Assume the samples were obtained independently from a large population using simple random sampling. Test whether p 1 greater than p 2. The sample data are x 1 equals 126​, n 1 equals 241​, x 2 equals 131​, and n 2 equals 302. ​(a) Choose the correct null and alternative hypotheses below. A. Upper H 0 : p 1 equals p 2 versus Upper H 1 : p 1 not equals p 2 B. Upper H 0 : p 1 equals 0 versus Upper H 1 : p 1 not equals 0 C. Upper H 0 : p 1 equals p 2 versus Upper H 1 : p 1 greater than p 2 Your answer is correct.D. Upper H 0 : p 1 equals p 2 versus Upper H 1 : p 1 less than p 2 ​(b) Determine the test statistic. Need to know the P-Value as well and the result of this hypothesis

Answer 1

a)

p1 = p2

p1 > p2

b)

sample #1   ----->              
first sample size,     n1=   241          
number of successes, sample 1 =     x1=   126          
proportion success of sample 1 , p̂1=   x1/n1=   0.5228          
                  
sample #2   ----->              
second sample size,     n2 =    302          
number of successes, sample 2 =     x2 =    131          
proportion success of sample 1 , p̂ 2=   x2/n2 =    0.4338          
                  
difference in sample proportions, p̂1 - p̂2 =     0.5228   -   0.4338   =   0.0890
                  
pooled proportion , p =   (x1+x2)/(n1+n2)=   0.4733          
                  
std error ,SE =    =SQRT(p*(1-p)*(1/n1+ 1/n2)=   0.0431          
Z-statistic = (p̂1 - p̂2)/SE = (   0.089   /   0.0431   ) =   2.0648

C)

p-value =        0.0195     [excel function =NORMSDIST(-z)]

decision :    p-value>α,Don't reject null hypothesis   

There is not enough evidence to conclude that  p 1 greater than p 2