Question

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 test 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.

Notation: 1= Year 2016 and 2=Year 2019
To use a normal distribution in this scenario, which of the following conditions must be satisfied?
Assume that the independence conditions are met.

Question 4 options:

	Both n2×pˆn2×p^ and n2×(1−pˆ)n2×(1-p^) must be at least 10 where pˆp^ is the pooled estimate for the common population proportion.
	Both n1×pˆn1×p^ and n1×(1−pˆ)n1×(1-p^) must be at least 10 where pˆp^ is the pooled estimate for the common population proportion.
	There must be at least 10 observed successes and 10 observed failures in the sample from Population 2.
	There must be at least 10 observed successes and 10 observed failures in the sample from Population 1.

Answer 1

We know that,

To use a normal distribution in this scenario,

There must be at least 10 observed “successes” and 10 observed “failures” in each group.

Hence,

There must be at least 10 observed successes and 10 observed failures in the sample from Population 2.
There must be at least 10 observed successes and 10 observed failures in the sample from Population 1.

i.e., Last two conditions must be satisfied.

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Thank you.