Proportion Confidence Interval

In statistics hypothesis testing are used to compute the probability for a particular hypothesis to be right. Hypothesis is specified as declaration which may or may not be precise. In statistics two hypothesis testing are consumed. They are null hypothesis and alternative hypothesis. The null and alternative hypotheses testing are opposed to every other. Various tests are used in statistics. The test of population proportionality is one of the most important in hypothesis testing. Confidence interval means we can specify the range. Let us see about the proportion confidence interval  .

Proportion confidence interval

The central confidence interval used for which the probability of being mistaken is separated uniformly into a range of proportions beneath the interval and another range exceeding the interval.

Confidence interval for proportion include the following steps

Confidence level

Sample size

Observed learn result

Assumptions

Proportion confidence intervals

When a 95% confidence interval is formed, each value in the interval is considered probable values for the parameter being expected. Values outer the interval are rejected as comparatively improbable.

If the value of the parameter illustrated through the null hypothesis is integrated in the 95% interval after that the null hypothesis cannot be rejected on the 0.05 level.

If the value specified through the null hypothesis is not contained through the interval afterward the null hypothesis is able to be rejected on the 0.05 level.

If a 99% confidence interval is formed, subsequently value outer the interval is rejected on the 0.01 level.

The formula used for 98% confidence limits for the proportion =`p+- 2.33sqrt((pq)/n)`

Examples for proportion confidence interval

A random sample of 600 oranges were obtained from a large consignment and 60 were of them are bad get the 98% confidence limits for the percentage number as bad oranges in the consignment.

Solution

98% confidence limits for the proportion `p+- 2.33sqrt((pq)/n)`

Calculation

Given n = 600, x = 60

p = `x/n = 60/600`

p = 0.1

p+q = 1

q = 1- 0.1

q = 0.9


By confidence limits for the proportion

`p+- 2.33sqrt((0.1xx0.9)/600)`

= 0.1 ± 0.0122

= 0.1122, 0.0878

Result

98% confidence limits for the percentage number as bad oranges in the consignment = [0.0878 x100, 0.1122 x 100]

= [8.78, 11.22]