Question

Effectiveness of online courses. The Survey of Online Learning, “Grade Level: Tracking Online Education in the United States, 2014,” reported that 74% of college leaders believe that their online education courses are as good as or superior to courses that use traditional, face-to-face instruction.

a. Give the null hypothesis for testing the claim made by the survey.

Short answer

a. The null hypothesis is, \({H_0}:p = 0.74.\)

Step-by-step solution

Given Information

74% of college leaders believe that their online education courses are as good as or superior to courses that use traditional, face-to-face instruction.

State the large sample test of the hypothesis about p.

The test statistic used to obtaining the large sample test of the hypothesis about p is,

\({Z_c} = \frac{{\left( {\hat p - {p_0}} \right)}}{{{\sigma _{\hat p}}}}\)

The condition required for a valid large sample hypothesis test for p are:

• The sample size n is large.
• A random sample is selected from a binomial population.

State the null hypothesis of the test.

a.

Let p be the true proportion of college leaders who believe that their online education courses are as good as or superior to courses that use traditional, face-to-face instruction.

The value of the p is computed as:

\(\begin{aligned}p = \frac{{74}}{{100}}\\ = 0.74\end{aligned}\)

The required null hypothesis is,\({H_0}:p = 0.74.\)

Hence, the null hypothesis is that the true proportion of college leaders who believe that their online education courses are as good as or superior to courses that use traditional, face-to-face instruction is 0.74.