Biff and Dilara were having an argument over what fraction of people would likel

Question

Biff and Dilara were having an argument over what fraction of people would likely go out of their way to drive over a live organism if it were standing innocently by the side of the road. Dilara, whose heart is pure, guessed that fewer than 2% of people would behave that badly- roughly the proportion of people who score as psychopaths in standard testing. Biff, who isn't revealing what he knows, guessed that the fraction would be higher, perhaps 5%. To settle the debate they analyzed data from an experiment in which a rubber fasciile of a turtle, a tarantula spider, a snake, or a leaf were placed on the paved shoulder of a two-way road. Of 1000 vehicles observed to drive by, 60 swerved onto the shoulder in an effort to dive over the rubber organism. Let's assume that each vehicle represents an independent trial and that thr probability of someone attempting to flatter the rubber organism is the same for each organism> Are these data consistent with a fraction of 2%? Are they consistent with a fraction of 5%?

Explanation / Answer

FOR 2%:

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value = 60/1000 =   0.06      

u = mean = p =    0.02      
          
s = standard deviation = sqrt(p(1-p)/n) =    0.004427189      
          
Thus,          
          
z = (x - u) / s =    9.035079029      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   9.035079029   ) =    0   

As it is a very small probbaility, then NO, IT IS NOT CONSISTENT WITH 2%. [ANSWER]

*********************************************************************************************************

FOR 5%:

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    0.06      
u = mean = p =    0.05      
          
s = standard deviation = sqrt(p(1-p)/n) =    0.006892024      
          
Thus,          
          
z = (x - u) / s =    1.4509525      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   1.4509525   ) =    0.073396544

As this probability is greater than 0.05, THEN YES, THE DATA IS CONSISTENT WITH THE FRACTION OF 5%. [ANSWER]

Related Questions

Navigate

• Browse (All)
• Browse B
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.