Question

About 77% of young adults think they can buy a house by the time they are 30. Determine if the following statements are true or false, and explain your reasoning.

(a) The distribution of sample proportions of young adults who think they can buy a house by the time they are 30, in random samples of size 40 is approximately normal since n ≥ 30.

(b) The distribution of sample proportions of young adults who think they can buy a house by the time they are 30, in samples of size 20 is left-skewed.

(c) A random sample of 60 young adults where 85% think they can buy a house by the time they are 30, would be considered unusual.

(d) A random sample of 120 young adults where 85% think they can buy a house by the time they are 30, would be considered unusual.

(e) The standard error would be reduced by one-half if we increased the sample size from 60 to 120.

Answer 1

(a) The distribution of sample proportions of young adults who think they can buy a house by the time they are 30, in random samples of size 40 is approximately normal since n ≥ 30.

1)True

(as np(1-p) is not greater than or equal to 10

(b) The distribution of sample proportions of young adults who think they can buy a house by the time they are 30, in samples of size 20 is left-skewed.

2) False

as that property is for sampling distribution of mean

(c) A random sample of 60 young adults where 85% think they can buy a house by the time they are 30, would be considered unusual.

3) False

as probabiltiy of that is greater than 0.05.

(d) A random sample of 120 young adults where 85% think they can buy a house by the time they are 30, would be considered unusual.

4) true