§2.The hypothesis testing of one normal population

Let denote a random sample from a normal distribution, is significance level. 1.Test of mean 1.1 Variance known The problem as follows When is true, then, thus So the critical region is. single normal population hypothesis testing

Example Let us assume,we have nine random samples, and the mean is 4.484,suppose the variance have no change, testing the following problem with the significance level. we get, Then can be accepted.

1.2 Variance unknown The problem as follows, When is true, then, Thus, So the critical region is.

Example Let us assume have normal distribution, we have 25 random samples, and the mean is 66.5,and the standard deviation of sample is 15, testing the following problem with the significance level. ， 2.06,,we get, Then can be accepted.

There are still two other kinds of problem of testing mean as follows

2.Test of variance The problem as follows When is true, then thus So the critical region is

Example Let us assume have normal distribution, we have 5 random samples, 1.32, 1.55, 1.36, 1.40, 1.44, and the standard deviation is, testing the following problem with the significance level From the given sample, we have hence, So we reject.

There are still two other kinds of problem of testing variance as follows ;