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

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.