Modul 1.2 – Distribusi Bernoulli

Summary

In this video script, the instructor guides students through an Excel-based Bernoulli experiment, where they perform calculations related to a binomial distribution using red (non-defective) and white (defective) buttons. The experiment includes two trials: with replacement and without replacement. Students record observations, calculate expected frequencies, and perform Chi-Square tests to determine whether the data follows a Bernoulli distribution. The process involves using Excel formulas for frequency and statistical analysis, with the final conclusion indicating whether the experiment's results fit the distribution model.

Takeaways

• 😀 The experiment involves using 30 buttons: 20 non-defective (red) and 10 defective (white), representing products in a manufacturing process.
• 😀 The objective is to test whether the observed frequencies of defective and non-defective products follow a Bernoulli distribution.
• 😀 The experiment is conducted in two ways: with replacement and without replacement, each repeated 10 times.
• 😀 In the 'with replacement' case, after each draw, the button is returned to the container; in the 'without replacement' case, buttons are not returned after being drawn.
• 😀 Students are instructed to record their observations (how many defective and non-defective buttons are drawn) in an Excel worksheet.
• 😀 The expected frequency is calculated using the formula: Expected Frequency = Probability * Number of Trials.
• 😀 The chi-square goodness-of-fit test is used to compare observed frequencies with expected frequencies to check if the data fits a Bernoulli distribution.
• 😀 To calculate chi-square, the formula used is: χ² = Σ[(Observed - Expected)² / Expected].
• 😀 The critical value for the chi-square test is taken from a chi-square distribution table based on the degree of freedom (df = number of categories - 1).
• 😀 If the chi-square calculated value is less than the chi-square critical value (3.841 for df=1), the null hypothesis (data follows Bernoulli distribution) is accepted.
• 😀 The use of Excel is emphasized for performing the calculations, including summing the expected frequencies and computing chi-square values.
• 😀 The results for both with and without replacement experiments are compared to ensure consistency and to validate the hypothesis.

Q & A

What is the purpose of the experiment described in the script?

The purpose of the experiment is to perform a binomial distribution test by drawing buttons (representing defective and non-defective products) from a jar. The experiment is done both with and without replacement to compare the observed results to the expected frequencies based on the binomial distribution.

What are the two types of experiments conducted in the script?

The two types of experiments are the 'with replacement' experiment and the 'without replacement' experiment, which involve drawing buttons from a jar either with or without putting the drawn button back into the jar.

How many buttons are used in the experiment and what do they represent?

A total of 30 buttons are used: 20 red buttons represent non-defective products, and 10 white buttons represent defective products.

What is the formula used to calculate the expected frequency for each type of button?

The formula used is: Expected Frequency = (Number of Red/White Buttons / Total Number of Buttons) * Total Trials.

What Excel formula is used to calculate the sum of the expected frequencies?

The Excel formula used is `=SUM()`, which adds the expected frequencies for the different types of buttons (red and white) across all trials.

How is the chi-square statistic calculated in the experiment?

The chi-square statistic is calculated using the formula: χ² = Σ[(O_i - E_i)² / E_i], where O_i is the observed frequency and E_i is the expected frequency for each outcome.

What does the chi-square test assess in this experiment?

The chi-square test assesses whether the observed frequencies of button draws (red and white) are significantly different from the expected frequencies based on the binomial distribution. If the chi-square value is smaller than the critical value, the null hypothesis that the data follows a binomial distribution is accepted.

What is the critical value of the chi-square statistic used in the experiment?

The critical chi-square value used in this experiment is 3.841, which corresponds to a significance level (alpha) of 0.05 and 1 degree of freedom.

What conclusion is drawn if the calculated chi-square value is smaller than the critical value?

If the calculated chi-square value is smaller than the critical value, the null hypothesis is accepted, meaning the data follows a binomial distribution.

What is the degree of freedom in this experiment, and how is it calculated?

The degree of freedom is calculated as the number of categories minus 1 (K - 1). Since there are two categories (red and white buttons), the degree of freedom is 1.