The student government claims that 70% of all students favor an increase in stud

Question

The student government claims that 70% of all students favor an increase in student fees to buy indoor potted plants for the classrooms. A random sample of 11 students produced 2 in favor of the project.

(a) What is the probability that 2 or fewer in the sample will favor the project, assuming the student government's claim is correct? (Use 3 decimal places.)

(b) Do the the data support the student government's claim, or does it seem that the percentage favoring the increase in fees is less than 70%? (pick one)

(i) The data seem to indicate that the percent favoring the increase in fees is less than 70%.

(ii) The data seem to indicate that the percent favoring the increase in fees is equal to 70%.    

(iii) The data do not give us any indication that the percent favoring the increase in fees differs from 70%.

(iv) The data seem to indicate that the percent favoring the increase in fees is greater than 70%.

Explanation / Answer

a)

Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    11      
p = the probability of a success =    0.7      
x = the maximum number of successes =    2      
          
Then the cumulative probability is          
          
P(at most   2   ) =    0.000577696 [ANSWER]

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b)

As this is a very small probability, this does not support the government's claim. 2 out of 11 is far lower than 70%. Hence,

OPTION I: (i) The data seem to indicate that the percent favoring the increase in fees is less than 70%.

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