Question

Select the answer for each. A random survey of 212 students asked each student to select the most preferred form of recreational activity from five choices. Here are the results of the survey: Basketball (1) Softball (2) Swimming (3) Jogging (4) Tennis (5) Male 31 16 19 22 23 Female 21 16 13 27 24 Does the true proportion of male students who prefer basketball exceed the true proportion of female students who prefer basketball? Approach this as the test about appropriate proportions. 1. The test statistic is [Select ] 2. The rejection region is [Select]

Answer 1

Ho:   p1 - p2 =   0
Ha:   p1 - p2 >   0
      
sample #1   ----->  
first sample size,     n1=   111
number of successes, sample 1 =     x1=   31
proportion success of sample 1 , p̂1=   x1/n1=   0.2793
      
sample #2   ----->  
second sample size,     n2 =    101
number of successes, sample 2 =     x2 =    21
proportion success of sample 1 , p̂ 2=   x2/n2 =    0.2079
      
difference in sample proportions, p̂1 - p̂2 =     0.2793-0.2079=   0.0714
      
pooled proportion , p =   (x1+x2)/(n1+n2)=   0.245283019
      
std error ,SE =    =SQRT(p*(1-p)*(1/n1+ 1/n2)=   0.05917
Z-statistic = (p̂1 - p̂2)/SE =     (0.0714-0)/0.0592=   1.2
1) test stat = 1.2

2) none of the answer given here