Modul 1.2 – Distribusi Bernoulli

Laboratorium Teknik Industri UMS
13 Nov 202413:42

Summary

TLDRIn 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.

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Étiquettes Connexes
Bernoulli TrialsExcel CalculationsData AnalysisStatistical TestingPractical ExperimentProbability TheoryExperiment ProcedureExcel TutorialFrequency AnalysisGoodness of FitScientific Method
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