9.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 H0 : p = .88. If Ha : p < .88, what's the corresponding P-value?

Step-by-step explanation:

For the null hypothesis,

H0: p = 88

For the alternative hypothesis,

Ha: p < 88

Considering the population proportion, probability of success, p = 0.88

q = probability of failure = 1 - p

q = 1 - 0.88 = 0.12

Considering the sample,

Sample proportion, P = x/n

Where

x = number of success = 21

n = number of samples = 32

P = 21/32 = 0.66

We would determine the test statistic which is the z score

z = (P - p)/√pq/n

z = (0.66 - 0.88)/√(0.88 × 0.12)/32 = - 3.83

The corresponding p value would be determined by looking at the normal distribution table for the area below the z score. Therefore,

P value = 0.00006

graph b

step-by-step explanation:

one solution- graph a (clear intercepting point.)

no solution- graph b (they're parallel, there will never be a point of interception.)

infinite solutions- graph c (all points intercept.)