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  2. AP Statistics
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What is the formula for Expected Count?

Expected Count = (Sample Size) x (Probability under Null Hypothesis)

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What is the formula for Expected Count?

Expected Count = (Sample Size) x (Probability under Null Hypothesis)

What is the formula for Chi-Square Statistic?

χ2=∑(Observed−Expected)2Expected\chi^2 = \sum \frac{(Observed - Expected)^2}{Expected}χ2=∑Expected(Observed−Expected)2​

What is the formula for Degrees of Freedom in a GOF test?

df = (Number of Categories) - 1

How to calculate expected count for movie series preference?

Expected Count = (Total Sample Size) * (Proportion under Null Hypothesis). E.g., for Harry Potter: 2500 * 0.33 = 825

What is the formula for calculating the chi-square statistic in the music preference example?

χ2=(180−200)2200+(150−150)2150+(170−150)2150\chi^2 = \frac{(180-200)^2}{200} + \frac{(150-150)^2}{150} + \frac{(170-150)^2}{150}χ2=200(180−200)2​+150(150−150)2​+150(170−150)2​

What are the differences between the Null Hypothesis and the Alternative Hypothesis in a GOF test?

Null Hypothesis (H0): The observed distribution matches the claimed distribution. | Alternative Hypothesis (Ha): At least one of the proportions in the null hypothesis is incorrect.

What are the differences between Observed Counts and Expected Counts?

Observed Counts: The actual data collected in each category. | Expected Counts: The values we anticipate seeing in each category if the null hypothesis is true.

What are the differences between a large chi-square value and a small chi-square value?

Large Chi-Square Value: Indicates a big difference between observed and expected counts, suggesting the null hypothesis might be false. | Small Chi-Square Value: Suggests the observed data is close to what's expected under the null hypothesis.

What are the differences between a small p-value and a large p-value?

Small p-value: Results are statistically significant, reject the null hypothesis. | Large p-value: Results are not statistically significant, fail to reject the null hypothesis.

What are the differences between conditions Random and Independence?

Random: Sample must be randomly selected. | Independence: Population must be at least 10 times the sample size (10% rule).

Explain the concept of a P-value in the context of a Chi-Square test.

The p-value tells us the probability of getting our observed results (or more extreme) if the null hypothesis were true. A small p-value (typically < 0.05) means our results are statistically significant, and we reject the null hypothesis.

Explain the concept of Chi-Square Distributions.

Chi-square distributions are always positive and skewed to the right. The shape is determined by the degrees of freedom; as df increases, the distribution becomes more symmetrical.

Explain the concept of the Large Counts condition for a GOF test.

The Large Counts condition requires that all expected counts must be at least 5. This ensures the chi-square statistic is approximately chi-square distributed.

Explain the purpose of the Random condition in a GOF test.

The sample must be randomly selected to ensure that the sample is representative of the population, which is a requirement for the GOF test to be valid.

Explain the purpose of the Independence condition in a GOF test.

The population must be at least 10 times the sample size (10% rule). This ensures that the observations are independent of each other.