Answer:
The correct answers are
1) There must be at least 10 observed successes and 10 observed failures in the sample from population 1.
3) There must be at least 10 observed successes and 10 observed failures in the sample from population 2.
Step-by-step explanation:
Hello!
You have two variables of interest:
X₁: Number of that had to put off medical treatment due to cost during 2016.
n₁= 967 people surveyed
x₁= 184 answered "yes"
sample proportion p'₁= 184/967= 0.19
X₂: Number of that had to put off medical treatment due to cost during 2019.
n₂= 1015 people surveyed
x₂= 253 answered "yes"
p'₂= 253/1015= 0.25
The pooled sample proportion is [tex]p'= \frac{x_1+x_2}{n_1+n_2} = \frac{184+253}{967+1015}= 0.22[/tex]
To study the population proportion you have to apply the Central Limit Theorem to approximate the distribution of the sample proportion to normal, the conditions for a valid approximation are:
Sample size n ≥ 30
n₁= 967
n₂= 1015
n*p'≥10 (each sample contains at least 10 successes)
n₁*p'₁= 967*0.19= 183.73
n₂*p'₂= 1015*0.25= 253.75
n*(1-p')≥10 (each sample contains at least 10 failures)
n₁*(1-p'₁)= 967*0.81= 783.27
n₂*(1-p'₂)= 1015*0.75= 761.25
The correct answers are
1) There must be at least 10 observed successes and 10 observed failures in the sample from population 1.
3) There must be at least 10 observed successes and 10 observed failures in the sample from population 2.
I hope it helps!
