Question

A researcher collects a sample of 15 measurements from a population and wishes to find a 90% confidence interval for the population mean. What value should he use for t*?

To find a 90% confidence interval for the population mean, he should use ______for t*.

Answer 1

With smaller samples i.e less than 30, the central limit theorem does not apply. For smaller sample another distribution known as t distribution is used. The t distribution is similar to the standard normal distribution. Depending on the sample size t distribution. T values are listed by degree of freedom (df). From t table a sample size of 15 would have degree of freedom. Degree of freedom is calculated by formula n-1. Here n=15, therefore, degree of freedom would be 15-1=14. Confidence interval is possible value for population parameters.

For 90% confidence interval, at degree of freedom 14, t will have value.

So to calculate ? we need to subtract confidence interval from 1. Symbol ? shows significance level. Value of ? shows the probability of accepting or rejecting null hypothesis. At 90 % significance level value of ? can be calculated as below:

? =1- 0.9

=0.1

In t table we need to see df 14 at ? 0.1.

Answer So in t table we need to check degree of freedom 14 at 0.1 ? value. Value of t using t table is 1.345 for one tail test and 1.761 for two tailed test.