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Section "Fundamentals of Mathematical Statistics". The topic is "Minimum or optimal sample size".

I offer you a mini-test.

Question One.

A randomly selected part of the parent population is called… Answer options…

Choose the correct answer. Question Two. A random sample is repetitive if… The answers are given.

Choose the correct answer.

Question Three. A sample population is non-repetitive if…

The answer options are given, choose the answer that you think is correct.

 Now let's check it out. Question One. The correct answer is the first one.

Question Two. The correct answer is number one. Question Three.

The correct answer is number two.

If a random re-selection is given, it is advisable to use the formula that is presented on the screen.

Explanatory notes are provided below. If a random non-repetitive sample is given, it is better to use the following formula.

Explanatory notes are also provided here. The simplest formula for finding the optimal sample size is now on the screen, explanatory notes are provided.

Here’s the task for you to solve using the last formula.

The effect of the therapeutic drug on the mass of mice is being studied.

After a month of testing in the experimental group, the weight of animals varied as follows: 80 g, 75 g, 62, 70, 68 and 71 g.

Determine with the accuracy of 1 g and with the reliability of 90% whether the number of mice in the experimental group is sufficient for the study to be reliable.

Let’s find the average value of the set sample.

Let's use the formula of the average for this. The average weight is 71 g.

Let’s find the corrected dispersion of the set sample using the formula. 

The corrected dispersion value is 37.6 G2. Let’s find the average and dipersion of the set sample in MS Excel.

Let's move our data to a worksheet in Excel and select Data on the Toolbar, then Data Analysis and select the Descriptive statistics procedure. The input interval.

Enter all the data.

Put a tick in the placemarks, since we have a title. Let’s mark the Final statistics and Reliability boxes.

Here the output interval is cell B1.

Note that the average value and dispersion of the sample (the corrected dispersion is calculated immediately here) have the same values that we obtained earlier using the formulas.

Now let’s find the value of the argument of the Laplace function. To do this, use the statistical function NORM.ST.OBR.

 Due to the fact that the reliability of 90% is given, which means that the confidence probability is 0.9, the probability will be presented as follows. Divide the confidence probability by 2 and add 0.5. The formula in this case looks like this…

This is nothing more than an argument to our function. The function value is 1.64.

This is the value of t. We take it approximately and substitute it into our formula. t=1.64 approximately. Corrected dispersion is 37.6.

The accuracy of the estimate (we have already mentioned this) is 1 g.

Note that rounding is carried out according to the statistical rule.

That's why the final answer is 102. We can't take 101, since the value of 101 is less than 101.13, so we take the largest one, in this case 102.

Thus, a sample of 102 mice will provide the specified accuracy and reliability. I offer tasks for independent solution. Task 1. Task. 2.

 I wish you success in solving them!

Thank you for your attention.