Statistical interpretation of data; Techniques of estimation and tests relating to means and variances of normal distributions

This standard specifies the methods for estimating the mean and variance of a population using a sample, and for testing certain assumptions about the mean and variance. GB 4889-1985 Statistical processing and interpretation of data Estimation and testing methods for the mean and variance of a normal distribution GB4889-1985 standard download decompression password: www.bzxz.net
This standard specifies the methods for estimating the mean and variance of a population using a sample, and for testing certain assumptions about the mean and variance.

1 Introduction
National Standard of the People's Republic of China
Statistical Interpretation of data
Estimation and test methods for means and varlarcesof normal distributions
UDC 51$.28
GB 4889-85
1.1 This standard specifies methods for estimating the mean and variance of a population using a sample, and for testing certain assumptions about the mean and variance. For the comparison of paired observations, see GB 3361-82 "Statistical treatment and interpretation of data - comparison of two means in the case of paired observations".
1.2 These methods are only valid when the sampling units are randomly and independently selected in each population under consideration. In the case of a finite population, when the size of the population is sufficiently large or the sampling proportion is sufficiently small (e.g. less than 1/10), the randomly selected sampling units can be considered independent.
1.8 This standard applies when the population distribution is normal. If the population distribution deviates slightly from normality and the sample size is not too small, the method described below is still approximately correct and its approximation is sufficient for most practical applications. For Tables 1, 3, 5, and 7, the sample size should be at least 5 to 10. For the other tables, the sample size should be not less than 20.
If the population distribution deviates significantly from normality, the variables can be transformed to be normal or nonparametric tests can be used. 1.4 The point estimate of the mean μ and variance of the population is given by the sample mean s and variance S?, respectively. 1.5 In the interval estimate of the mean μ and variance of the population, the confidence level 1-α is the probability that the confidence interval contains the true value of the estimated parameter. The confidence level 1~α value is usually 0.95 or 0.99, that is, α=0.05 or 0.01.1.6 In hypothesis testing, for two-sided cases, the significance level is the probability of rejecting this hypothesis when the null hypothesis is established (the probability of type I error), and for one-sided cases, the significance level is the maximum of the above probabilities (the maximum probability of type 1 error). α0.05 or α=0.01 is a commonly used value according to the different risks that the user is prepared to bear. Because a hypothesis may be rejected when using α=0.05, but may not be rejected when using α=0.01, the statement "this hypothesis is rejected at the 5% level" is adopted, or in the latter case, the statement "this hypothesis is rejected at the 1% level" is adopted. If the null hypothesis is not established but is accepted, a type II error is committed.
1.7 Individual suspicious data cannot be arbitrarily eliminated or corrected. For specific treatment methods, see GB4883--85 "Statistical Processing and Interpretation of Data Normal Sample Outliers Judgment and Treatment". 1.8 In statistical calculations, relevant information such as the source and collection method of the observations should be given. 1.9 In statistical calculations, the calculations can often be simplified by changing the origin or units. 1.10 This standard is formulated with reference to the international standard ISO2854 "Statistical interpretation of data - methods for estimating and testing means and variances" (first edition in 1976).
Issued by the National Bureau of Standards on January 29, 1985
Implemented on October 1, 1985
2 Calculation tables
Technical characteristics of the population
Technical characteristics of the sampling unit
Obviously eliminated observations
Statistical items
Sample size:
Sum of observations:
≥x,=
Given value:
GB 4889---85
Comparison of mean and given value (variance known) Table 1
Known values ​​of population variance:
Standard deviation:
Significance level:
Population mean u and given value μ. Comparison of
Two-sided case:
If {-μo「>（u-ai2l/n）
then reject the null hypothesis that the population mean is equal to the given value. One-sided case,
a. If <μo-（u-an）α
then reject the null hypothesis that the population mean is not less than the given value. b. If x+（u,=aljn）
then reject the null hypothesis that the population mean is not greater than the given value. Note:
U represents the standard normal variable, u. The value is defined as a, Www.bzxZ.net
p(Uu.)=1-α
Ma/= - w[-a/2
Two-sided case
GB 4889-80
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