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 condition doesn't need to be met before using a two-sample procedure, let's analyze each statement one by one:
1. The responses in each group are independent of each other.
Explanation: Independence of responses is a necessary condition for using a two-sample procedure. If the responses in each group are not independent, it can introduce bias or affect the validity of the analysis. Therefore, this condition must be met before using a two-sample procedure.
2. Each group is considered to be a sample from a distinct population.
Explanation: This condition also needs to be met before using a two-sample procedure. If the two groups are not samples from distinct populations, it may not be appropriate to compare their means using a two-sample procedure. So, this condition must be met.
3. The same variable is measured in both samples.
Explanation: This condition is essential for conducting a two-sample procedure. Comparing means of the two groups requires the same variable to be measured in both samples. If different variables are measured, it wouldn't make sense to use a two-sample procedure to compare their means.
4. The goal is to compare the means of the two groups.
Explanation: This condition is necessary, as it specifies the purpose of using a two-sample procedure. If the goal is not to compare the means of the two groups, then a two-sample procedure might not be suitable.
5. Data in two samples are matched together in pairs that are compared.
Explanation: This condition describes a paired/dependent two-sample procedure, where the data in the two samples are matched or paired together. However, not all two-sample procedures require matching pairs. There are also independent two-sample procedures where matching is not needed. So, this condition does not need to be met in all two-sample procedures.
From the above analysis, it can be concluded that the condition "Data in two samples are matched together in pairs that are compared" is the one that doesn't need to be met before using a two-sample procedure.
Now, let's analyze the given statements:
I. We use one-sample procedures when our samples are equal in size but aren't independent.
Explanation: This statement is true. One-sample procedures can be used even when the samples are equal in size but are not independent. One-sample procedures compare a sample mean to a known or hypothesized population mean.
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.
Explanation: This statement is true. With all other factors being equal, as the degrees of freedom increase, the t-distribution becomes more similar to the standard normal distribution. A narrower confidence interval can be obtained with higher degrees of freedom.
III. The samples used in all two-sample procedures must be of the same size.
Explanation: This statement is false. The samples used in two-sample procedures do not always need to be of the same size. The sample sizes can differ, and the specific analysis used will depend on the design and objectives of the study.
Based on the analysis, the correct answer is II only.