A middle school held a three-day sports meeting in the new century, and at the same time held a whole school spiritual civilization competition, in order to let all the teachers and students know abou

A middle school held a three-day sports meeting in the new century, and at the same time held a whole school spiritual civilization competition, in order to let all the teachers and students know about this activity. Solution: (1) Because this activity has different impacts on faculty, junior high school students and senior high school students, stratified sampling should be adopted for sampling.

∫ The sample size is 120, and the total is 500+3000+4000=7500.

Then the sampling ratio is

= 8 (name),

=48 (name),

=64 (name),

The number of individuals selected from teachers, junior high school students and senior high school students is 8, 48 and 64 respectively.

The steps of stratified sampling are:

① Stratification: divided into three layers: teaching staff, junior high school students and senior high school students.

② Determine the number of individuals selected from each floor: the number of individuals selected from teaching staff, junior high school students and senior high school students is 8, 48 and 64 respectively;

(3) Sampling each layer by simple random sampling method;

(4) synthesizing samples of all layers to form samples,

In this way, the whole sampling process is completed, and a more objective evaluation conclusion can be drawn.

(2) Because there are two methods of simple random sampling: the lottery method or the random number method, if the lottery method is adopted, it will take a lot of effort to make the membership fee of 3000 numbers, so the random number method is adopted for sampling, and the steps are as follows:

① numbering: number all 3000 answers: 000 1, 0002, …, 3000;

② Randomly select a starting position on the random number table;

(3) Specify the reading direction: read the numbers continuously (take the right as an example), with four numbers as a group. When touching the right line, connect the left line of the next line and continue to take numbers to the right. If the four digits read are greater than 3,000, delete them. If you encounter the same number, just take one number, and so on until 48 numbers are filled;

(3) Because 4000÷64=62.5 is not an integer, we should randomly select 32 individuals from 4000 students by simple random sampling, and then number the remaining 3968 individuals as: 1, 2, …, 3968, and then divide the whole into 64 parts, each containing 62 individuals, such as the first part of individuals. If 23 is selected, starting from the 23rd, choose one for every 62 numbers, and the sample sizes thus obtained are 64: 23, 85, 147, 209, 27 1, 333, 395, 457, …, 3 929.