Question

Recently the U.S. Department of Education released a report on online learning stating that blended instruction, a combination of conventional face-to-face and online instruction, appears more effective in terms of student performance than conventional teaching. You decide to poll the incoming students at your institution to see if they prefer courses that blend face-to-face instruction with online components. In an SRS of 300 incoming students, you find that 213 prefer this type of course.

(a) What is the sample proportion who prefer this type of blended instruction? (Round your answer to two decimal places.)

(b) If the population proportion for all students nationwide is 85%, what is the standard deviation of p̂? (Round your answer to four decimal places.) σp̂ = ?

(c) Using the 68–95–99.7 rule, if you had drawn an SRS from the United States, you would expect p̂ to fall between what two percents about 95% of the time? (Round your answers to two decimal places.)

Answer 1

Solution

Given that,

(a)

sample proportion = 213 / 300 = 0.71

(b)

p = 0.85

1 - p = 0.15

n = 300

The mean of the sampling distribution of proportion is ,

= p = 0.85

The standard deviation of the sampling distribution is ,  

=  [p( 1 - p ) / n = [(0.85 * 0.15) / 300] = 0.0206

(c)

P(   - 2< p <   + 2) = 95%

P(0.85 - 2 * 0.0206 < p < 0.85 + 2 * 0.0206) = 95%

P(0.81 < p < 0.89) = 95%