Question

About 77% of young adults think they can achieve the American dream. Determine if the following statements are true or false. You may use the embedded Shiny app to explore the shape of the distribution for differing values of n and p.

1. The distribution of sample proportions of young Americans who think they can achieve the American dream in samples of size 20 is left skewed.  ? True False

2. 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.  ? True False

3. A random sample of 60 young Americans where 85% think they can achieve the American dream would be considered unusual. ? True False

4. A random sample of 120 young Americans where 85% think they can achieve the American dream would be considered unusual.

Answer 1

Solution:-

1. The distribution of sample proportions of young Americans who think they can achieve the American dream in samples of size 20 is left skewed. --> True.

2.  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. --> Flase

3. A random sample of 60 young Americans where 85% think they can achieve the American dream would be considered unusual. --> Flase

  --> less tha 2,so is not unusual.

4. 4. A random sample of 120 young Americans where 85% think they can achieve the American dream would be considered unusual. --> True