Your mathematics instructor claims that, over the years, 88% of his students have said that math is their favorite class. In this year's class, however, only 21 out of 32 students named math as their favorite. The teacher decides to conduct a test of the hypothesis Ho: p = 88 If Ha: p < 0.88 what's the corresponding P-value?

Question

A. 0.00

B. .08

C. .96

D. 1738
Ε. 0869

Answer 1

To find the corresponding P-value, we can use a one-sample proportion z-test.

First, calculate the sample proportion:
p̂ = x/n
p̂ = 21/32
p̂ ≈ 0.656

Next, calculate the standard error (SE) of the sample proportion:
SE = √(p*(1-p)/n)
SE = √(0.88*0.12/32)
SE ≈ 0.054

Next, calculate the z-score:
z = (p̂ - p) / SE
z = (0.656 - 0.88) / 0.054
z ≈ -4.222

Now, we find the corresponding P-value using a standard normal distribution table or calculator. The P-value for a z-score of -4.222 is approximately 0.00.

Therefore, the corresponding P-value is A. 0.00.