Solution Found!
A national poll of 549 teenagers (aged 13 to 17) by the
Chapter 3, Problem 176E(choose chapter or problem)
Problem 176E
A national poll of 549 teenagers (aged 13 to 17) by the Gallop poll (http://gallup.com/conten/ default.aspx?ci=17110), April, 2005) indicated that 85% “think that clothes that display gang symbols” should be banned at school. If teenagers were really evenly split in their opinions regarding banning of clothes that display gang symbols, comment on the probability of observing this survey result (that is, observing 85% or more in a sample of 549 who are in favor of banning clothes that display gang symbols). What assumption must be made about the sampling procedure in order to calculate this probability? [Hint: Recall Tchebysheff’s theorem and the empirical rule.]
Questions & Answers
QUESTION:
Problem 176E
A national poll of 549 teenagers (aged 13 to 17) by the Gallop poll (http://gallup.com/conten/ default.aspx?ci=17110), April, 2005) indicated that 85% “think that clothes that display gang symbols” should be banned at school. If teenagers were really evenly split in their opinions regarding banning of clothes that display gang symbols, comment on the probability of observing this survey result (that is, observing 85% or more in a sample of 549 who are in favor of banning clothes that display gang symbols). What assumption must be made about the sampling procedure in order to calculate this probability? [Hint: Recall Tchebysheff’s theorem and the empirical rule.]
ANSWER:
Solution:
Step 1 of 2:
In a poll of 549 teenagers, 85% “think that clothes display gang symbols” should be banned at school.
The claim is to comment on the probability of observing the survey result and the assumption must be made about the sampling procedure in order to calculate this probability.
Where, n = 549 and p = 0.5
Let X follows the Binomial distribution with probability mass function
P(x) = , x = 0, 1, 2, ....