Statistics: Confidence Intervals

In summary, a confidence interval is a range of values used to estimate the unknown value of a population based on a sample of data. It is important because it provides a measure of precision and allows for comparisons between groups. It is calculated using the sample mean, standard deviation, and sample size. The confidence level represents the level of uncertainty in the estimate and cannot be used to make a definitive conclusion about the population parameter.
  • #1
jlo2006
3
0
Heres the problem:

Mr. K would like to know what percentage of the senior class has watched the movie Groundhog Day. He would like to be sure to within 0.05 or 5%. He wants to compute a 90% confidence interval. How many students must he poll in order to achieve these goals?

Help Please. Greatly Appreciated.
 
Physics news on Phys.org

What is a confidence interval?

A confidence interval is a range of values that is likely to include the true population parameter with a specific degree of certainty (usually 95%). It is a statistical measure used to estimate the unknown value of a population based on a sample of data.

Why are confidence intervals important?

Confidence intervals are important because they provide a measure of the precision of an estimate. They help us determine how confident we can be that our sample statistic is close to the true population parameter. They also allow us to compare different groups or samples and make inferences about the population.

How is a confidence interval calculated?

A confidence interval is calculated using the sample mean, standard deviation, and sample size. The formula is: sample mean ± (critical value x standard error), where the critical value is determined by the desired level of confidence and the standard error is a measure of the variability of the sample.

What is the significance of the confidence level in a confidence interval?

The confidence level in a confidence interval represents the degree of uncertainty we are willing to accept in our estimate. It is typically expressed as a percentage (e.g. 95%) and determines the width of the confidence interval. A higher confidence level means a wider interval, but also a greater degree of certainty in our estimate.

Can a confidence interval be used to make a definitive conclusion about the population parameter?

No, a confidence interval cannot be used to make a definitive conclusion about the population parameter. It only provides an estimate of the true value with a certain level of confidence. To make a definitive conclusion, further research or a larger sample size may be needed.

Similar threads

Confidence intervals for ratios of variances and other confusing stats
    • Calculus and Beyond Homework Help
Replies
5
Views
1K
Confusion between z and t values
    • Calculus and Beyond Homework Help
Replies
5
Views
2K
Statistics Confidence Intervals Question?
    • Calculus and Beyond Homework Help
Replies
1
Views
1K
Confidence interval of two sample tests
    • Calculus and Beyond Homework Help
Replies
4
Views
4K
I Time intervals measured by stationary and moving observers
    • Special and General Relativity
2
Replies
43
Views
2K
What is the confidence interval if the sample size is 30 instead?
    • Calculus and Beyond Homework Help
Replies
7
Views
2K
B Chebyshev inequality, confidence intervals, etc
    • Set Theory, Logic, Probability, Statistics
Replies
6
Views
3K
Confidence interval for a cohort
    • Calculus and Beyond Homework Help
Replies
10
Views
4K
Tdistribution to construct a confidence interval question
    • Calculus and Beyond Homework Help
Replies
2
Views
2K
Finding a confidence interval.
    • Calculus and Beyond Homework Help
Replies
1
Views
6K

Hot Threads

Recent Insights

Back
Top