Question

The Mathematics department was interested in determining if the results of online classes were different than that of face-to-face classes. A SRS of 250 online students found that 183 passed they were taking. If the proportion of students taking their classes in a live classroom setting and passing them is 79%, test the appropriate claim at the 0.05 level of significance.

a)     Formulate the appropriate claim.

b)    Calculate the test statistic.

c)     Find the p-value.

d)    Formulate the conclusion statistically.

e)    Formulate the conclusion practically.

Answer 1

Solution:

a)

H₀ : p = 0.79

H_a : p 0.79 (Claim)

b)

Let   be the sample proportion.

= x/n = 183/250  = 0.732

The test statistic z is

z =   

=  (0.2423 - 0.2)/[0.2*(1 - 0.2)/227]

= -2.25

3)

TWO TAILED TEST

p value = P(Z < -z) + P(Z > +z) = P(Z < -2.25) + P(Z > +2.25) = 0.0122+0.0122 = 0.0244

p value is 0.0244

4)

Reject H₀:

Because p value is less than 0.05 level of significance.

5)

There is sufficient evidence to conclude that the results of online classes were different than that of face-to-face classes.