Suppose 21% of all American teens (age 13-17 years) believe in reincarnation.

(a)    Bob and Alicia both obtain a random sample of 100 American teens and ask each participant to disclose whether they believe in reincarnation or not. Is "belief in reincarnation" qualitative or quantitative? Explain.

(b)    Explain why Bob's sample of 100 randomly selected American teens might result in 18 who believe in reincarnation, while Alicia's independent sample of 100 randomly selected American teens might result in 22 who believe in reincarnation. 

(c)    Why is it important to randomly select American teens to estimate the population proportion who believe in reincarnation? 

(d)    In a survey of 100 American teens, how many would you expect to believe in reincarnation? 

(e)    Below is the histogram of the sample proportion of 1000 different surveys in which n = 20 American teens were asked to disclose whether they believed in reincarnation. Explain why the normal model should not be used to describe the distribution of the sample proportion.

(f)What minimum sample size would you require in order for the distribution of the sample proportion to be modeled by the normal distribution?

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Frequency 200 150 100 50 0.3 0.1 0.2 0.4 0.5 0.6 p-hat