Join the IDNLearn.com community and start exploring a world of knowledge today. Ask anything and receive prompt, well-informed answers from our community of knowledgeable experts.
Sagot :
Certainly! Let's interpret the given 95% confidence interval for the difference in proportions between the members of political party B and political party A.
Here are the steps:
1. Determine the Confidence Interval:
- We are given that the 95% confidence interval for the difference in proportions is [tex]\((-0.11\)[/tex] to [tex]\(-0.03)\)[/tex], or in terms of percentage points, [tex]\((-11\%\)[/tex] to [tex]\(-3\%\)[/tex]).
2. Check if the Interval Includes Zero:
- The interval ranges from [tex]\(-0.11\)[/tex] to [tex]\(-0.03\)[/tex]. Since 0 is not within this range (i.e., 0 is not between [tex]\(-0.11\)[/tex] and [tex]\(-0.03\)[/tex]), the confidence interval does not contain zero.
3. Interpret the Negative Values in the Interval:
- Because the confidence interval consists of only negative values, this indicates that, with 95% confidence, the proportion of members of political party B who agreed with the statement is lower than the proportion of members of political party A who agreed with the statement.
4. Summarize the Interpretation:
- The negative values suggest that party B has a lower agreement rate with the statement compared to party A.
Therefore, the interpretation of the confidence interval is as follows:
"The difference in proportions (party B - party A) is between [tex]\(-0.11\)[/tex] and [tex]\(-0.03\)[/tex]. Since the interval does not include 0, we can conclude at a 95% confidence level that the proportion of members of political party B who agree with the statement is lower than that of the members of political party A."
To fill in the blanks in the statement:
- "that the difference in proportions (party B - party A) is between [tex]\(\-0.11\)[/tex] and [tex]\(\-0.03\)[/tex][tex]\(\)[/tex]."
So, the completed statement is:
- “The difference in proportions (party B - party A) is between -0.11 and -0.03.”
Additionally,
- If the interval contains 0, it means that: the difference in proportions cannot be conclusively said to be different from zero at the 95% confidence level (i.e., there could be no significant difference).
- The meaning of positive and/or negative values: Negative values indicate that party B has a lower agreement rate than party A, while positive values would indicate the reverse.
Therefore, we can summarize that the interval never contains zero, indicating a clear difference in proportions, and in this case, party B’s agreement rate is lower than that of party A.
Here are the steps:
1. Determine the Confidence Interval:
- We are given that the 95% confidence interval for the difference in proportions is [tex]\((-0.11\)[/tex] to [tex]\(-0.03)\)[/tex], or in terms of percentage points, [tex]\((-11\%\)[/tex] to [tex]\(-3\%\)[/tex]).
2. Check if the Interval Includes Zero:
- The interval ranges from [tex]\(-0.11\)[/tex] to [tex]\(-0.03\)[/tex]. Since 0 is not within this range (i.e., 0 is not between [tex]\(-0.11\)[/tex] and [tex]\(-0.03\)[/tex]), the confidence interval does not contain zero.
3. Interpret the Negative Values in the Interval:
- Because the confidence interval consists of only negative values, this indicates that, with 95% confidence, the proportion of members of political party B who agreed with the statement is lower than the proportion of members of political party A who agreed with the statement.
4. Summarize the Interpretation:
- The negative values suggest that party B has a lower agreement rate with the statement compared to party A.
Therefore, the interpretation of the confidence interval is as follows:
"The difference in proportions (party B - party A) is between [tex]\(-0.11\)[/tex] and [tex]\(-0.03\)[/tex]. Since the interval does not include 0, we can conclude at a 95% confidence level that the proportion of members of political party B who agree with the statement is lower than that of the members of political party A."
To fill in the blanks in the statement:
- "that the difference in proportions (party B - party A) is between [tex]\(\-0.11\)[/tex] and [tex]\(\-0.03\)[/tex][tex]\(\)[/tex]."
So, the completed statement is:
- “The difference in proportions (party B - party A) is between -0.11 and -0.03.”
Additionally,
- If the interval contains 0, it means that: the difference in proportions cannot be conclusively said to be different from zero at the 95% confidence level (i.e., there could be no significant difference).
- The meaning of positive and/or negative values: Negative values indicate that party B has a lower agreement rate than party A, while positive values would indicate the reverse.
Therefore, we can summarize that the interval never contains zero, indicating a clear difference in proportions, and in this case, party B’s agreement rate is lower than that of party A.
Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. IDNLearn.com is your source for precise answers. Thank you for visiting, and we look forward to helping you again soon.
