Question

define confidence interval and degree of confidence. provide at least one example of a confidence interval and interpret the result. Please give an example so i can also understand thank you!

Answer 1

Confidence intervals are often used with a margin of error. It tells you how confident you can be that the results from a poll or survey reflect what you would expect to find if it were possible to survey the entire population. Confidence intervals are intrinsically connected to confidence levels.

In general manner, Confidence interval tells you how confident you can that the results falls in your true data.

Degree of confidence represents the probability that the confidence interval captures the true population parameter.

With a degree of confidence of 95%, you have 95% confidence that the true population parameters will be in the confidence interval.

Suppose. You have data where sample mean=25, standard deviation =9 and n=9. And level of significance 0.05 i.e.95%confidence then value of confidence interval is

The formula for estimation is:

μ = M ± Z(sM)
where:

M = sample mean
Z = Z statistic determined by confidence level
sM = standard error = √(s2/n)

M = 25
Z = 1.96 by using z table
sM = √(92/45) = 1.34

μ = M ± Z(sM)
μ = 25 ± 1.96*1.34
μ = 25 ± 2.63

You can be 95% confident that the population mean (μ) falls between 22.37 and 27.63.