6.2 Young Americans, Part I. About 77% ofyoung adults think they can achieve the
ID: 3310889 • Letter: 6
Question
6.2 Young Americans, Part I. About 77% ofyoung adults think they can achieve the American dream. Determine if the following statements are true or false, and explain your reasoning.3 (a) The distribution of sample proportions of young Americans who think they can achieve the (b) The distribution of sample proportions of young Ar (c) A random sample of 60 young Americans where 85% think they can achieve the American (d) A random sam ple of 120 young Americans where 85% think they can achieve the American American dream in samples of size 20 is left skewed. American dream in random samples of size 40 is approximately normal since n 30. dream would be considered unusual. dream would be considered unusual. who think they can achieve theExplanation / Answer
About 77% of young adults think they can achieve the American dream. Determine if the following statements are true or false, and explain your reasoning.
(a)The distribution of sample proportions of young Americans who think they can achieve the
American dream in samples of size 20 is left skewed.
Ans:False. It considered to be slightly left skewed, but the proportion of values
is less than 0.01, so the sample is very close to normal
(b) The distribution of sample proportions of young Americans who think they can achieve the
American dream in random samples of size 40 is approximately normal since n> 30.
Ans:False. The reason is not that n30. For proportions we need to consider the success-
fail condition. THe sample size =40 the success is 40*0.77=30.8,the failure is 40*0.23=9.2
(c) A random sample of 60 young Americans where 85% think they can achieve the American
dream would be considered unusual.
Ans:False. The proportion of the time a sample of size 60 would yield 85% or more under
the assumption that 77% of the population think they can achieve the American dream
is 0.0893191, which is greater than 0.05
(d) A random sample of 120 young Americans where 85% think they can achieve the American
dream would be considered unusual
Ans:True. The proportion of the time a sample of size 120 would yield 85% or more under
the assumption that 77% of the population think they can achieve the American dream
is 0.020506, which is less than 0.05. Even under a two-sided test would be considered
unusual
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