Cost of Health Care ~ Have you or a member of your immediate family put off medical treatment due to cost during the past year? In 2016, a survey asked 967 randomly selected American adults this question and 184 said yes. In 2019, another survey asked the same question to 1015 randomly selected American adults and 253 said yes. We want to determine if there is a difference between the proportion of Year 2016 American adults and Year 2019 American adults, who put off medical treatment due to cost.

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

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!

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