Which of the following conditions doesn't need to be met before you can use a two-sample procedure?



The responses in each group are independent of each other.

Each group is considered to be a sample from a distinct population.

The same variable is measured in both samples.

The goal is to compare the means of the two groups.

Data in two samples are matched together in pairs that are compared.

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Which of the following statements is false?
I. We use one-sample procedures when our samples are equal in size but aren't independent.

II. Everything else being equal, a confidence interval based on 15 degrees of freedom will be narrower than one based on 10 degrees of freedom.

III. The samples used in all two-sample procedures must be of the same size.



I only

II only

III only

I and III only

None of the above gives the correct response.

3 only

To answer these questions, let's look at each option and statement individually.

For the first question, the conditions that need to be met before you can use a two-sample procedure are:

1. The responses in each group are independent of each other.
2. Each group is considered to be a sample from a distinct population.
3. The same variable is measured in both samples.
4. The goal is to compare the means of the two groups.
5. Data in two samples are matched together in pairs that are compared.

Out of these options, the condition that doesn't need to be met before you can use a two-sample procedure is "Data in two samples are matched together in pairs that are compared." This condition refers to paired data, where measurements or observations are made on the same subjects in both groups, such as before and after treatment.

Therefore, the correct answer to the first question is: "Data in two samples are matched together in pairs that are compared."

For the second question, let's analyze each statement:

I. We use one-sample procedures when our samples are equal in size but aren't independent.
This statement is true. One-sample procedures can be used when comparing a single sample to a known value, and independence is not a requirement.

II. Everything else being equal, a confidence interval based on 15 degrees of freedom will be narrower than one based on 10 degrees of freedom.
This statement is false. As the degrees of freedom increase, the confidence interval tends to become wider, not narrower. A larger degrees of freedom value indicates a larger sample size, which gives more precision and reduces uncertainty.

III. The samples used in all two-sample procedures must be of the same size.
This statement is false. While it is not necessary for the samples to be of the same size in all two-sample procedures, it is often desirable to have balanced sample sizes if possible for better comparability.

Therefore, the correct answer to the second question is: "III only."

To summarize:
1. For the first question, the condition that doesn't need to be met before you can use a two-sample procedure is "Data in two samples are matched together in pairs that are compared."
2. For the second question, the false statement is "III only."