Question

What is the relationship between confidence intervals and levels of significance? Please provide an example other then, the most common use application of confidence interval and confidence level is in market research. Thank you

Answer 1

Confidence intervals are range of values that the population parameters (mean, std dev) can take. It is confidence interval because the range is not 100% accurate. It has some level of confidence eg 95%. So we read it as :95% confident that the popualtion mean would lie within (a, b). The reason for this inaccuracy is that these values are based on a sample and not the entire population.

Level og significance is like the probability of error associated with the confidence interval. So if we are 95% sure about the interval then, we have 5% chance of error that is the population parameter is outside this range with probability of 5%.

Example: Population the people of XYZ city and their incomes.

Population = 1000000

Sample = 100

95% confidence level for mean income of the city is ($40000, $60000).

Different parameters have different distribution. If the population SD is known then for mean normal distribution is used otherwise t-dist. For the variance itself ch-square distribution is used. For ratio of variances F-dist is used.