# Confidence Interval (CI)

This webpagina assumes that for means and standard deviation the sample gegevens comes from a corriente distribution. For proportions, the habitual distribution approximates the binomial for n x P(hat) is greater than or equal to Five.

Sample statistics such spil the mean, standard deviation and proportion (x-bar, s, p-bar) are only estimates of the population parameters.

CI’s are used when you are incapable to capture and analyze an entire population (census) and the sample (statistics) to infer statements about a population. The larger your sample size, the more confidence one can be that their answers represent the population. Tho’ the relationships are not linear, the larger the sample size the smaller the confidence interval (more certain you can be that it the true population parameters will fall within a tighter spectrum).

The size of the population is a cifra when working with a relatively petite and known group of gegevens (such spil the number of lumps of candy te a bag frente a the number of fish te the ocean).

The CI calculations assume you have a true random sample of the population. If the sample is not then one cannot rely on the confidence intervals calculated, because you can no longer rely on the measures of central tendency and dispersion.

The accuracy of the CI also depends on the percentage of your sample that picks a particular response. If 99.9% of the parts sampled PASSED and the 0.1% FAILED, the chances of error are very low regardless of sample size.

However, if the percentages are 51% and 49% the chances of error are much greater. It is lighter to be sure of extreme answers than those aren’t, thus the interval is not linear.

## Confidence Interval for the Mean

The CI for the mean represents the sample mean +/- confidence coeficiente * a measure of variability.

sample mean = 45 minutes

sample standard deviation = Five.8 minutes

Alpha-risk = 1-CI = 1-0.99 = 0.01

The critical t-value from the table using two tailed is Two.831

(Recall to take the alpha-risk/Two when using the t-table)

### What does this tell us?

This is telling us that the point estimate of the promedio wait time is 45 minutes with an error of +/- Five.8 minutes. There is 99% certainty that the interval <41.Five minutes to 48.Five minutes>contains the true process mean. There is a 1% chance that this decision is wrong.

## Excel to calculate Confidence Interval

You can use Excel to find only the CI for a population mean. The population standard deviation voorwaarde be known. Excel uses the Z-table to reference te its calculation.

Population Standard Deviation = 6.48

Sample Size = 27

Sample Mean (x-bar) = 50

Knowing that you determined your sample mean (x-bar) to be 50, add Two.44 to get the upper limit of the interval and subtract Two.44 to get the lower limit of the interval and that becomes the CI for the population mean.

### Confidence Interval for the Standard Deviation

The chi-squared distribution is not symmetrical and each varies according the degrees of freedom, dF.

Calculate the population standard deviation using a 95% confidence level. Assume the population is known to be normally distributed.

The media wage of \$38.73 is not needed for the CI calculation.

## Confidence Interval for Proportions

Many business decisions involve population proportions such spil estimating market share and proportions of goods that are acceptable or defective.

p-hat = 153/300 = 51% = 0.51

The critical Z(0.04) value = 1.75

The CI states that with 92% confidence, the proportion of all similar companies with the project will inbetween 46% and 56%.

## Confidence Interval for Capability

To determine the CI for process capability use the formula provided below where:

LSL = customer lower specification limit

Click here to purchase slips that suggest more information regarding confidence intervals. Often, statistics are not voiced te terms of one number but rather spil a range or an interval with a given level of confidence.

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