Part 1: Some of the methods in this section are approximations rather than exact
ID: 2932883 • Letter: P
Question
Part 1: Some of the methods in this section are approximations rather than exact probability results. We have given rules of thumb for safe use of these approximations.
(a) You are interested in attitudes toward drinking among the 75 members of a fraternity. You choose 30 members at random to interview. One question is "Have you had five or more drinks at one time during the last week?" Suppose that in fact 30% of the 75 members would say "Yes." Explain why you cannot safely use the B(30, 0.3) distribution for the count X in your sample who say "Yes."
The population (the 75 members of the fraternity) is only 2.5 times the size of the sample. Our rule of thumb says that this ratio should be at least [ANSWER] .
(b) The National AIDS Behavioral Surveys found that 0.2% (that's 0.002 as a decimal fraction) of adult heterosexuals had both received a blood transfusion and had a sexual partner from a group at high risk of AIDS. Suppose that this national proportion holds for your region. Explain why you cannot safely use the Normal approximation for the sample proportion who fall in this group when you interview an SRS of 1000 adults.
Our rule of thumb for the Normal approximation calls for np and n(1 p) to be at least [ANSWER] ; we have np = (1000)(0.002) = 2.
Part 2: 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 400 incoming students, you find that 317 prefer this type of course.
(c) Using the 68–95–99.7 rule, if you had drawn an SRS from the United States, you would expect p to fall between what two percents about 95% of the time? (Round your answers to two decimal places.)
( %, %)
Explanation / Answer
Ans:
a)The population (the 75 members of the fraternity) is only 2.5 times the size of the sample. Our rule of thumb says that this ratio should be at least 10.
The 10% condition states that sample sizes should be no more than 10% of the population.
b)For normal approximation:
np>=10 and n(1-p)>=10
As,here np=1000*0.002=2<10
So,normal approximation is not valid.
c)samle proportion=317/400=0.79
Using the 68–95–99.7 rule,95% of the data falls within 2 standard deviations.
95% CI
=0.79+/-2*sqrt(0.79*(1-0.79)/400)
=0.79+/-2*0.02
=0.79+/-0.04
=(0.75,0.83)