Math Problem Statement

a random sample of 100 adults were asked if they pay for monthly subscriptions. with a 95% confidence interval for the true proportion of adults who pay for subscriptions they do not use is .352 to 0.548. What is the point estimate and margin of error?

Solution

The confidence interval provided for the true proportion of adults who pay for subscriptions they do not use is from 0.352 to 0.548.

1. Point Estimate:

The point estimate of the proportion is the sample proportion p^\hat{p}, which is the midpoint of the confidence interval.

To calculate the point estimate: p^=0.352+0.5482=0.45\hat{p} = \frac{0.352 + 0.548}{2} = 0.45

So, the point estimate is 0.45.

2. Margin of Error:

The margin of error (MOE) is half the width of the confidence interval. To calculate this, subtract the lower bound from the upper bound and then divide by 2: Margin of Error=0.5480.3522=0.098\text{Margin of Error} = \frac{0.548 - 0.352}{2} = 0.098

Thus, the margin of error is 0.098.


Summary:

  • Point Estimate: 0.45
  • Margin of Error: 0.098

Would you like more details on how to calculate these values, or do you have any other questions?

Here are some related questions you might find useful:

  1. How does the confidence level affect the margin of error in statistical estimates?
  2. What is the formula for calculating the margin of error for a proportion?
  3. How can you interpret a confidence interval for a proportion in terms of population estimates?
  4. What other methods can be used to estimate a population proportion?
  5. How do sample size and variability impact the width of a confidence interval?

Tip: In general, the wider the confidence interval, the more uncertainty there is about the true population parameter. Reducing the margin of error typically requires increasing the sample size.

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Math Problem Analysis

Mathematical Concepts

Confidence Interval
Proportions
Margin of Error
Point Estimate

Formulas

Point Estimate (\hat{p}) = (Lower Bound + Upper Bound) / 2
Margin of Error (MOE) = (Upper Bound - Lower Bound) / 2

Theorems

Confidence Interval for Proportions
Properties of Estimators

Suitable Grade Level

Grades 9-12