Statistics Confidence Intervals Question?

In summary, a Gallup Poll in 2002 found that 25% of adults reported experiencing a crime in the past year, with a margin of sampling error of +/- 3 percentage points. Among respondents aged 18-29 years, 43% had been victims of a crime. The margin of error for this age group is most likely larger than +/- 3 percentage points due to the smaller sample size, but the exact calculation would require knowing the confidence interval width provided by Gallup. To achieve the same confidence interval for 18-24 year olds, a larger sample size would be needed.
  • #1
mintsnapple
50
0

Homework Statement


A Gallup Poll of 1002 adults in October 2002 found that 25% of the respondents said that their household
had experienced a crime in the past year. Among respondents aged 18-29 years, 43% had been victims of a
crime. Gallup says, “For results based on the total sample of national adults, one can say with 95%
confidence that the margin of sampling error is +/- 3 percentage points.” Is the margin of error for adults
aged 18-29 smaller than, larger than, or the same as +/- 3 percentage points?


Homework Equations





The Attempt at a Solution


Well, I think because of the smaller sample size, the margin of error would be larger because it is less precise. Yet, this sample size comes from a larger sample size with a given confidence interval width, so I am not sure.
 
Physics news on Phys.org
  • #2
Hi mintsapple!

Do you know how to calculate the confidence limit that Gallup provided? Can you calculate how big a sample of 18-24 year olds yu would need to get the same confidence interval?
 

Related to Statistics Confidence Intervals Question?

1. What is a confidence interval in statistics?

A confidence interval in statistics is a range of values that is likely to contain the true value of a population parameter with a certain level of confidence. It is typically expressed as a percentage, such as 95% confidence interval.

2. How is a confidence interval calculated?

A confidence interval is calculated using the sample data and the desired level of confidence. The formula for calculating a confidence interval varies depending on the type of data and the statistical test being used. In general, it involves determining the margin of error and adding or subtracting it from the sample statistic.

3. What does the confidence level mean?

The confidence level refers to the percentage of times the calculated confidence interval would contain the true population parameter if the same population was sampled and the same process was repeated. For example, a 95% confidence level means that if we were to take 100 samples from the same population and calculate 95% confidence intervals, 95 of those intervals would contain the true population parameter.

4. What is the difference between confidence interval and margin of error?

The margin of error is the amount of error that is expected in an estimate due to random sampling. It is typically represented as a plus or minus value and is used to calculate the confidence interval. The confidence interval, on the other hand, is a range of values that is likely to contain the true population parameter with a certain level of confidence. It takes into account the margin of error and is a more precise measure of uncertainty.

5. Why is it important to report confidence intervals in statistical analysis?

Reporting confidence intervals in statistical analysis is important because it provides a measure of the precision of the estimate and the level of uncertainty in the data. It also allows for comparison between different studies and helps to determine the practical significance of the results. Additionally, it helps to identify any potential biases or errors in the data and allows for more informed decision making based on the results.

Similar threads

Confusion between z and t values
    • Calculus and Beyond Homework Help
Replies
5
Views
2K
MHB Confidence interval of difference
    • Set Theory, Logic, Probability, Statistics
Replies
1
Views
687
Tdistribution to construct a confidence interval question
    • Calculus and Beyond Homework Help
Replies
2
Views
2K
Confidence interval for a cohort
    • Calculus and Beyond Homework Help
Replies
10
Views
4K
Questions related to sufficient statistics and confidence interval
    • Precalculus Mathematics Homework Help
Replies
1
Views
2K
I T-distribution, standard error - how to interpret
    • Set Theory, Logic, Probability, Statistics
Replies
7
Views
2K
MHB Are These Statistics Practice Answers Correct?
    • General Math
Replies
1
Views
1K
Confidence interval interpretation mistake
    • Set Theory, Logic, Probability, Statistics
Replies
24
Views
4K
Confidence interval/statistic question
    • Set Theory, Logic, Probability, Statistics
Replies
2
Views
1K
Statistics help, Confidence interval
    • Engineering and Comp Sci Homework Help
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top