Population mean
In different condition the population mean may results in different way
Let us consider two different condition in which population mean have to test.
One is when population variance is known and other is when population variance is unknown.
When population variance is known, Let
Null hypothesis is equal to or less than 20
Alternative hypothesis is greater than 20
The known significance level is .05, Hence, type one error should not exceed .05.
We also know that probability of type one error will highest when meu is in breakpoint,
Another two test should proceed,
One tailed test
two tailed test
Let us consider,
Null hypothesis is equal to 20
Alternative hypothesis not equal to 20
The significance level is equal to .05
One tailed test implies in that situation when critical region place under the one tail, specially right tail shaded area. In contrast with two tail test the critical region places under both tail of the distribution.
In codition of null hypothesis equal to 20 and alternative hypothesis not equal to 20, when null hypothesis should be reject. only then null hypothesis should be reject when test statics be more deviate from the value 20. Otherwise, not.
The signioficance level .05 indicates that the total pkrobability of rejecting null hypothesis is .05. The critical region exixt in both tail is equal and its value is .25
The lower limit of the accepktence region ia mu - 1.96sigma/rootover n
The uppker limit of the accepktence region is mu - 1.96sigma/root n