5.66 Attitudes toward drinking and studies of behavior. 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. (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.
5.66 Attitudes toward drinking and studies of behavior. 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. (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.
MATLAB: An Introduction with Applications
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Question
![5.66 Attitudes toward drinking and studies of behavior.
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.
(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.
PRODA](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F44b767e2-6751-4234-b8c8-6ae85db4f11d%2Fc8bfe0da-f24c-44a6-9e75-e74045ff32b4%2Fj2lmgna_processed.jpeg&w=3840&q=75)
Transcribed Image Text:5.66 Attitudes toward drinking and studies of behavior.
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.
(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.
PRODA
Expert Solution
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Step 1
The question is about approximation
Introduction :
Normal approximation to the binomial distribution
The binomial distribution tends to normal distribution if
i ) n * p > 5
ii ) n * ( 1- p ) > 5
Normal approximation for sample proportion :
Sample prop. tends to normal distribution if
i ) n * p > 10
ii ) n * ( 1 - p ) > 10
To find :
Explain for given problem approximation is need to use or not
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