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.
To determine which conditions need to be met before using a two-sample procedure, let's examine each statement:
1. The responses in each group are independent of each other.
This is a necessary condition for using a two-sample procedure. When the responses in each group are independent, it allows for valid statistical inference.
2. Each group is considered to be a sample from a distinct population.
This is also a necessary condition for using a two-sample procedure. The two samples being compared should represent different underlying populations to make meaningful comparisons.
3. The same variable is measured in both samples.
This condition needs to be met for conducting a two-sample procedure. The goal is to compare the means of the two groups on the same variable.
4. The goal is to compare the means of the two groups.
This condition is explicitly stating the purpose of the two-sample procedure. It is essential to clarify that the goal is to compare the means and not some other statistics or parameters.
5. Data in two samples are matched together in pairs that are compared.
This condition is not required for a two-sample procedure. If the data in two samples are matched together in pairs, it suggests a paired or dependent samples design, which requires a different type of analysis.
From the analysis above, it is evident that the condition that doesn't need to be met before using a two-sample procedure is: "Data in two samples are matched together in pairs that are compared."
Therefore, the correct choice is: Data in two samples are matched together in pairs that are compared.
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Now, let's evaluate the statements to determine which one is false:
I. We use one-sample procedures when our samples are equal in size but aren't independent.
This statement is true. One-sample procedures are suitable for cases where the samples are not independent, but the samples' sizes are equal.
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 true. As the degrees of freedom increase, the width of the confidence interval decreases, resulting in a narrower interval.
III. The samples used in all two-sample procedures must be of the same size.
This statement is false. Two-sample procedures can be conducted with samples of different sizes. Although equal sample sizes provide certain advantages, it is not a requirement for all two-sample procedures.
Based on the evaluation above, the correct answer is: III only.