Difference between confidence interval and significance level

Please explain the difference between confidence interval and significance level and how they interact or "influence" each other.

Could you please give me a clear explanation with a simple example of these concepts.

Solution Preview

Please see the attached files.

Confidence interval is associated with interval estimation and significance level is associated with testing of hypothesis. (Note that confidence interval is a random interval that contains the true parameter with a specified probability). Associated with a confidence interval there is a confidence level or confidence coefficient. It is to be noted that the interval estimation and testing of hypothesis are two parallel developments in Statistics. It is easy to see the following result.
Confidence level of a confidence interval = 1 - significance level of the associated test.
i.e. Confidence level of a confidence interval = 1- Î±, where Î± is the significance level of the associated test.
To make the concepts clear first, I will provide the procedure for finding a confidence interval and test construction:

Construction of a confidence interval for a parameter Î¸ Construction of test associated with the parameter Î¸
Step 1: Fix the confidence level for the interval. Let it be 1-Î±

Step 2: Select a suitable statistic, say t, containing the parameter Î¸ and identify its ...

Solution Summary

The differences between confidence interval and significance levels are examined.

Assume that in a hypothesis test with null hypothesis H 0: mu = 14.0 at alpha = 0.05, that a value of 13.0 for the sample mean results in the null hypothesis being rejected. That corresponds to a confidenceinterval result of:
a) the 95% confidenceinterval for the mean contains the value 14.0
b) the 95% confidenceinterval

A confidenceinterval for the population mean tells us which values of mean are plausible (those inside the interval) and which values are not plausible (those outside the interval) at the chosen level of confidence. You can use this idea to carry out a test of any null hypothesis. Ho:mean =Mo starting with a confidence interva

I need help solving the following problems:
In this problem set you will get some practice performing hypothesis tests for two samples. If you use Statdisk to perform any portion of these analyses, please include the results, label them, and refer to them accordingly in your interpretations. Good luck and enjoy!
1. Ten

We are evaluating the sheet metal scrap rate in a contractor proposal. Based on a sample of 28 parts you calculate a mean rate of 6.50% (treat as 6.50) and a standard deviation of 1.20. Calculate a 80% confidenceinterval to be used to support negotiations. (Carry intermediate calculations to three decimal places.)
6.18 â

Suppose that, for a sample size n = -100 measurements, we find that x = 50. Assuming that the standard deviation equals 2, calculate confidenceintervals for the population mean with the following confidencelevels:
a) 95% b) 99% c) 97% d) 80% e) 99.73% f) 92%

Which of the following is not needed to be known to calculate a confidenceinterval?
a. standard deviation
b. sample size
c. mean
d. degree of confidence

1. What are the null and alternate hypotheses for this test? Why?
2. What is the critical value for this hypothesis test using a 5% significancelevel?
3. Calculate the test statistic and the p-value using a 5% significancelevel.
4. State the decision for this test.
5. Determine the confidenceintervallevel that would be a

What would be the 95% confidenceinterval for this difference?
95% CI = mean difference +/- 2(standard error of the difference)
t = 5.185
df = 13201
mean dif = -.16
Std. Error Dif = .031
95% CI (lower -.221)
(upper -.100)

A. In a random sample of 500 people aged 20-24, 22% were smokers. In a random sample of 450 people aged 25-29, 14% were smokers. Construct a 95% confidenceinterval for the differencebetween the population proportions. You may assume the samples are independent.
You will be asked to identify each of the following.
1. Th