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

Ο Ε. 0869

Answer 1

B. .08

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

First, calculate the sample proportion:
p-hat = x/n = 21/32 = 0.65625

Next, calculate the test statistic:
z = (p-hat - p) / √(p(1-p)/n)
z = (0.65625 - 0.88) / √(0.88(1-0.88)/32)
z = -3.39

Now, we can find the corresponding P-value using a standard normal distribution table or calculator.

P-value = P(Z < -3.39) = 0.0003

Therefore, the corresponding P-value is approximately 0.0003, which is equivalent to 0.08%. So, the correct answer is B. .08.