standard normal table critical value
Chapter 4, probability distribution and sampling distribution - Presentation Transcript Chapter 4, probability distribution and sampling distribution sampling distribution 4.2 4.1 probability learning objectives of this chapter Home Excel discrete random variable probability distribution function Excel worksheet continuous probability distribution of random variable The use of Excel worksheet functions to draw a normal distribution graph Excel worksheet functions random distribution of the probability distribution of 4.1, probability and probability distribution 4.1.1 4.1.2 4.1.1 Binomial Distribution 4.1.3 Normal distribution probability and the probability of return to home page Excel provides the distribution of discrete probability distribution, including: BINOMDIST: binomial CRITBINOM: cumulative binomial distribution (according to the critical value, find the smallest integer K) HYPGEOMDIST: hypergeometric distribution NEGBINOMDIST: negative binomial POISSON: Poisson Excel provides a continuous distribution of probability distribution, including: BETADIST: cumulative probability density function BETAINV: cumulative probability density function of the inverse function EXPONDIST: exponential distribution function GAMMADIST: Gamma distribution function GAMMAINV: Gamma cumulative distribution function of the inverse function LOGNORMDIST: lognormal cumulative distribution function LOGINV: lognormal cumulative distribution function of the inverse function NORMDIST: normal distribution function NORMINV: normal cumulative distribution function of the inverse function NORMSDIST: standard normal cumulative distribution function NORMSINV: standard normal cumulative distribution function of the inverse function WEIBULL: Weibull distribution function returns the binomial distribution 1 of this section 4.1.2. Binomial distribution function 2. Cumulative binomial distribution function 3. Negative binomial distribution function 1. Binomial distribution function of binomial distribution function for the fixed number of independent trials, when the test results include only two cases when the success or failure, and when the probability of success during the trial is fixed, the function returns a binomial distribution probability value, which is calculated as the syntax: BINOMDIST (number_s, trials, probability_s, cumulative) cases of coin flip results 4-1 is negative than positive, as positive if the probability of each coin is 0.5. Then flip a coin 10 times in the 6 times the probability of a positive number? (1) the establishment of "BINOMDIST function. Xls" worksheet, enter the data shown in Figure 4-1. (2) in cell C2 enter the formula "= BINOMDIST (B2, B3, B4, FALSE)", press the Enter key to display the result is equal to 0.205078, as shown in Figure 4-2. Toss 10 coins, it said the probability of 0.205078 6. Figure 4-1 BINOMDIST function worksheet function to calculate the results of Figure 4-2 BINOMDIST 2. Cumulative binomial distribution function of the cumulative binomial distribution function to calculate the critical value is greater than or equal to the smallest integer value. Cumulative binomial distribution function can be used for quality inspection. For example, use the function to determine the maximum allowed CRITBINOM number of defective parts, it can guarantee the product when leaving the assembly line inspection. Syntax: CRITBINOM (trials, probability_s, alpha) Figure 4-3 CRITBINOM function worksheet function to calculate the results of Figure 4-4 CRITBINOM 3. Negative binomial distribution function which returns the negative binomial distribution. When the success probability is constant probability_s, the function NEGBINOMDIST number_s successful return before the arrival, there number_f the probability of failures. This function is similar to the binomial distribution function, but its success is the number of fixed total number of test variables. With the binomial distribution is similar to the test number is assumed to be independent variables, the formula is: Syntax: NEGBINOMDIST (number_f, number_s, probability_s) Figure 4-5 NEGBINOMDIST Figure 4-6 NEGBINOMDIST worksheet functions function returns the result Section 4.1.3 The normal distribution 1. Normal distribution function 2. Draw a normal distribution graph 1. Normal distribution function (1) normal distribution function. (2) the standard normal distribution function. (3) the inverse function of normal distribution function. (4) the inverse function of the standard normal distribution function. 2. Draw normal graphics (1) the establishment of the normal distribution of basic data. (2) Draw a normal distribution graph. Figure 4-7 "sequence" dialog box Figure 4-8 showed that (4 ~ 117 lines hidden) Figure 4-9 "Format Axis" dialog box, Figure 4-10 "Format Data Series" dialog box Figure 4-11 normal mapping the results of the sampling distribution of returns in this section 4.2 4.2.1 4.2.2 sampling process simulation using Excel overall distribution and sampling distribution of central limit theorem 4.2.3 4.2.1 4.2.4 t distribution process through the use of Excel simulated sampling sampling methods, to be produced by the mother samples taken following a capacity of 10 samples. Figure 4-12 Figure 4-13 to establish a working table of random numbers generated integral function dialog box Figure 4-14 Figure 4-15 Figure 4-16 Parameters dialog box selected index function returns the sample results dialog box Figure 4-17 overall this section 4.2.2 distribution and sampling distribution sampling distribution of the overall distribution and relationship between a certain number, the number of relations can be described as: that the mean of the sampling distribution of sample means is equal to the population mean;, the sample mean variance of the sampling distribution of the population variance divided by the sample size is equal to the square root, that is, the standard error of this type is also known, is the standard deviation of sampling distribution. Back to section 4.2.3 of this central limit theorem in probability and statistics, the normal distribution plays an important role, many random variables follow a normal distribution, even if the original does not follow a normal number of independent random variables, when a random variable unlimited number of increases, and the distribution of their normal distribution. Back to this section 4.2.4 t distribution 11. t distribution function of the function is used in a certain level of freedom and obtained significant probability of t distribution area. t distribution for small sample data sets, hypothesis testing, use this function instead of t distribution critical values table. Syntax: TDIST (x, degrees_freedom, tails) 2. t distribution function returns the inverse function of the probability and the degrees of freedom as a function of t = t distribution. Syntax: TINV (probability, degrees_freedom) where: probability for the two-tailed t distribution corresponding to the probability, degrees_freedom for the distribution of degrees of freedom. Back to this section
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Z distribution. X2 distribution. T distribution. F distribution.
Cumulative binomial distribution table value
Tables cumulative Poisson distribution
Standard normal density function table
Standard normal distribution function table
Bilateral normal distribution critical values table
Bilateral t distribution critical values table
X2 distribution table on the side of the critical value X2a
F distribution critical values table on the side
The critical value of correlation coefficient test table
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6. Binomial distribution
Understand the two tests should meet the four conditions; understanding of binomial probability formula; understanding of the mathematical expectation and variance of the binomial distribution; flexible use of the binomial distribution to solve practical problems.
Understanding normal and standard normal distribution; learn how to be a normal distribution into a standard normal distribution; understand graphical features of the normal distribution; master the standard normal distribution table; understand the amount of data with normal distribution and standard deviation of the number of relationship; flexible use of the normal distribution to solve practical problems.
(E) sampling and estimate population parameters
Learn the meaning and principles of sampling design; understand several important sampling method. Understanding of sampling error and the maximum permissible error of the concepts.
2. Sample distribution
Sample distribution to understand the meaning and the concept of standard error; understand the law of the distribution of sample mean (central limit theorem), flexible use of it to solve practical problems; understand the sample variance, sample variance than the distribution law; understand the standard error (SE) concept ; understand the distribution of the four theories, including the standard normal distribution (Z distribution), t distribution, chi-square distribution and F distribution, master them graphics features, will be the critical value for the corresponding table.
3. Point estimate
Understand the concept of point estimates and point estimates should meet four conditions. Understand the concept of statistics and parameters and their differences and links.
4. Interval Estimation
Understand the range of estimates, confidence intervals, confidence level, the concepts of significance level; understand the point and interval estimation of the strengths and weaknesses, differences and linkages.
5. The overall estimate of the average
Proficiency in a general average of the estimates, regardless of whether it is state of the overall variance is known, a large sample or small sample. Estimated according to the conditional distribution of statistic is Z or t, and the corresponding standard errors.
6. The overall estimate of the proportion of
Proficiency in large samples an overall proportion of point and interval estimation, understanding of the corresponding standard errors.
7. Estimated that the overall proportion of the overall average and to determine when the sample size
Grasp the overall average and the overall estimated proportion method for determining the sample size n.
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