An advertisement for a body lotion claims that 83% of its users reports smoother and softer skin after two weeks. The results of the survey are accurate within 3.5 percent points, 4 out of 5 times. What is the confidence interval?

To determine the confidence interval for the percentage of users reporting smoother and softer skin, we need to consider the given percentage and the margin of error. Here's how we can calculate it:

1. **Reported Percentage (\( p \))**: 83% or 0.83
2. **Margin of Error (\( E \))**: 3.5 percentage points or 0.035
3. **Confidence Level**: The phrase "4 out of 5 times" implies an 80% confidence level.

The confidence interval is calculated using the following formula:

\[ \text{Confidence Interval} = \left( p - E, p + E \right) \]

Plugging in the values:

\[ p = 0.83 \]
\[ E = 0.035 \]

The lower bound of the confidence interval is:

\[ 0.83 - 0.035 = 0.795 \]

The upper bound of the confidence interval is:

\[ 0.83 + 0.035 = 0.865 \]

Therefore, the confidence interval is:

\[ (0.795, 0.865) \]

**Conclusion**:
The confidence interval for the percentage of users reporting smoother and softer skin after two weeks is 79.5% to 86.5%.

Would you like more details or have any questions about this calculation? Here are some other questions you might find interesting:

1. How do we calculate confidence intervals for different confidence levels?
2. What is the significance of the margin of error in a survey?
3. How can we interpret the confidence interval in real-world scenarios?
4. What factors can affect the accuracy of survey results?
5. How do we determine the sample size required for a desired margin of error?

**Tip**: Understanding how to interpret confidence intervals can provide valuable insights into the reliability of survey results and statistical estimates.

Learn how to calculate the confidence interval for a survey claiming 83% of users report smoother and softer skin after two weeks. Understand the statistical concepts involved, including margin of error and confidence level. Suitable for advanced high school students and beyond.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation