Your mathematics instructor claims that, over the years, 88% of his students have said that math is their favorite subject. In this year's class, however, only 21 out of 32 students named math as their favorite class. The teacher decides to conduct a test of the hypothesis Ho: p = 0.88 . What's the correct value of the standard deviation of p for this test?

Question

Your mathematics instructor claims that, over the years, 88% of his students have said that math is their favorite subject. In this year's class, however, only 21 out of 32 students named math as their favorite class. The teacher decides to conduct a test of the hypothesis Ho: p = 0.88 . What's the correct value of the standard deviation of p for this test?

A. 045

B. .088

C. .057

D. 073

Ε. .064

Answer 1

To calculate the standard deviation of p for this test, we will use the formula:

Standard deviation of p = sqrt( (p*(1-p)) / n )

Where:
p = proportion of students who named math as their favorite subject (in this case, 21/32)
n = sample size (in this case, 32)

First, calculate p:
p = 21/32
p = 0.65625

Now, plug p and n into the formula:

Standard deviation of p = sqrt( (0.65625*(1-0.65625)) / 32 )
Standard deviation of p = sqrt( (0.65625*0.34375) / 32 )
Standard deviation of p = sqrt( 0.22507324218 / 32 )
Standard deviation of p = sqrt( 0.007033537569 )
Standard deviation of p ≈ 0.084

Therefore, the correct value of the standard deviation of p for this test is around 0.084. None of the given options match exactly, but the closest one is B. .088 with a slight rounding difference.