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.
For the first question, 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." So the answer is:
Data in two samples are matched together in pairs that are compared.
For the second question, the statement that is false is "III. The samples used in all two-sample procedures must be of the same size." So the answer is:
III only
To determine which condition doesn't need to be met before you can use a two-sample procedure, let's analyze each option:
1. The responses in each group are independent of each other. - This condition is essential for conducting a two-sample procedure. If the responses are not independent, it may affect the validity of the statistical analysis.
2. Each group is considered to be a sample from a distinct population. - This condition is also required for a two-sample procedure. The two groups being compared should come from different populations to make meaningful comparisons.
3. The same variable is measured in both samples. - This condition is crucial for a two-sample procedure. To compare the means of two groups, the same variable needs to be measured in both samples.
4. The goal is to compare the means of the two groups. - This is the purpose of a two-sample procedure. If the goal is not to compare means, then a different type of analysis may be more appropriate.
5. Data in two samples are matched together in pairs that are compared. - This condition describes a specific type of two-sample procedure called a paired or matched sample t-test. However, it is not necessary for all two-sample procedures. Other methods, like the independent sample t-test, do not require matched pairs.
Based on the explanations above, the condition that doesn't need to be met before you can use a two-sample procedure is:
Option 5: Data in two samples are matched together in pairs that are compared.
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Now let's analyze the statements provided:
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 in situations where samples are equal in size but not 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. - This statement is true. As the degrees of freedom increase, the width of the confidence interval tends to decrease, resulting in a narrower interval.
III. The samples used in all two-sample procedures must be of the same size. - This statement is false. The samples used in two-sample procedures can have different sizes. Unequal sample sizes are accommodated in statistical analyses through appropriate statistical tests and adjustments.
Based on the explanations above, the false statement is:
Option III only.
Therefore, the correct response is: III only.