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.
