A report noted that for the population of 9th graders,one-third of the students are unable to pass a quiz in basic geography.One teacher,having spent a great deal of time on geography instruction,gave the same quiz to a group of n = 72.Only X = 18 students in the group did not pass the test.The teacher would like to know if the number of students in this class who failed the quiz is significantly different from the general population.For this test,what is the z-score corresponding to X = 18?
A)z = 0.375
B)z = -1.00
C)z = -1.50
D)z = 2.00

Question

A report noted that for the population of 9th graders,one-third of the students are unable to pass a quiz in basic geography.One teacher,having spent a great deal of time on geography instruction,gave the same quiz to a group of n = 72.Only X = 18 students in the group did not pass the test.The teacher would like to know if the number of students in this class who failed the quiz is significantly different from the general population.For this test,what is the z-score corresponding to X = 18?​
A)​z = 0.375
B)​z = -1.00
C)​z = -1.50
D)​z = 2.00

Quizplus · Accepted Answer

To calculate the z-score, we need to use the formula:

z = (X - μ) / σ

where X is the number of students in the class who failed the quiz, μ is the mean proportion of students who fail the quiz in the general population (which is 1/3), and σ is the standard deviation of the population, which we assume to be:

σ = sqrt[(1/3)(2/3) / n]

where n is the sample size (which is 72 in this case).

Plugging in the numbers, we get:

z = (18 - (1/3)*72) / sqrt[(1/3)(2/3) / 72] 
  = -1.5

Therefore, the z-score for X = 18 is -1.50.

A Report Noted That for the Population of 9th Graders,one-Third