7.1.7 Chi-Squared Test

Cards (75)

  • The degrees of freedom in a Chi-Squared Test are calculated as the number of categories minus one.

    True
  • Steps in stating the null and alternative hypotheses for a Chi-Squared Test
    1️⃣ Define the null hypothesis (H₀)
    2️⃣ Define the alternative hypothesis (H₁)
  • The Chi-Squared statistic is calculated using the formula \chi^{2} = \sum \frac{(O - E)^{2}}{E}</latex>.

    True
  • If the calculated Chi-Squared value exceeds the critical value, the null hypothesis is rejected.

    True
  • Steps to calculate expected values for a Chi-Squared Test
    1️⃣ Total Observed (TO)
    2️⃣ Total Expected (TE)
    3️⃣ Grand Total
    4️⃣ Calculate Expected Value (E)
  • The significance level represents the probability of rejecting a true null hypothesis.

    True
  • What is the significance level in hypothesis testing?
    Probability of Type I error
  • A significance level of 0.01 corresponds to a Type I error probability of 1
  • Steps in performing the Chi-Squared Test
    1️⃣ Calculate the Chi-Squared statistic
    2️⃣ Determine the degrees of freedom
    3️⃣ Choose a significance level
    4️⃣ Find the critical value
    5️⃣ Compare the calculated statistic to the critical value
  • The degrees of freedom in a Chi-Squared Test are calculated as the number of categories minus one.

    True
  • What happens to the null hypothesis if the calculated Chi-Squared statistic exceeds the critical value?
    It is rejected
  • The alternative hypothesis in a Chi-Squared Test posits that there is a significant difference between observed and expected data.
    True
  • What is the formula to calculate expected values in a Chi-Squared Test?
    E = \frac{TO \times TE_{\text{category}}}{GT}</latex>
  • In the example provided, the grand total (\(GT\)) is 240.

    True
  • What is the confidence level associated with a significance level of 0.05?
    95%
  • The Chi-Squared statistic is calculated using the formula \chi^{2} = \sum \frac{(O - E)^{2}}{E}</latex>, where \(O\) is the observed frequency and \(E\) is the expected frequency
  • What should you do if the calculated Chi-Squared statistic is greater than the critical value?
    Reject the null hypothesis
  • Steps to apply the Chi-Squared formula
    1️⃣ Calculate the Chi-Squared statistic
    2️⃣ Determine the degrees of freedom
    3️⃣ Choose a significance level
    4️⃣ Find the critical value
    5️⃣ Compare the Chi-Squared statistic to the critical value
  • The degrees of freedom (\( df \)) are calculated by subtracting 1 from the number of categories
  • If the calculated Chi-Squared statistic is greater than the critical value, you reject the null hypothesis.
    True
  • What is the calculated Chi-Squared statistic in the genetic study example?
    4
  • Since the Chi-Squared statistic (4) is greater than the critical value (3.84), we reject the null hypothesis
  • The formula for calculating degrees of freedom in the Chi-Squared Test is \( df = (\text{Number of Categories} - 1)\).
    True
  • Match the Chi-Squared Test conclusion with the corresponding condition:
    Calculated Chi-Squared Statistic > Critical Value ↔️ Reject the null hypothesis
    Calculated Chi-Squared Statistic ≤ Critical Value ↔️ Fail to reject the null hypothesis
  • What does the null hypothesis state in a Chi-Squared Test?
    No significant difference
  • The Chi-Squared Test tests the null
  • The significance level in a Chi-Squared Test is typically 0.05
  • Match the hypothesis with its statement for a Chi-Squared Test:
    Null (H₀) ↔️ There is no significant difference between observed and expected data
    Alternative (H₁) ↔️ There is a significant difference between observed and expected data
  • The degrees of freedom in a Chi-Squared Test are calculated as the number of categories minus one
  • Match the hypothesis with its statement for a Chi-Squared Test:
    Null (H₀) ↔️ No significant difference
    Alternative (H₁) ↔️ Significant difference
  • The formula for calculating expected values is E = \frac{TO \times \text{TE for category}}{\text{Grand Total}}</latex>, where TO is the total observed, TE is the total expected, and Grand Total is the sum of all frequencies
  • A significance level of 0.05 corresponds to a confidence level of 95%
  • The significance level is the probability of rejecting the null hypothesis when it is true.
    True
  • Match the significance level with its corresponding confidence level:
    0.05 ↔️ 95%
    0.01 ↔️ 99%
  • The Chi-Squared statistic is calculated using the formula χ2=\chi^{2} =∑(O−E)2E \sum \frac{(O - E)^{2}}{E}, where O represents the observed frequency and E represents the expected
  • In the Chi-Squared Test, the null hypothesis states that there is no significant difference between observed and expected
  • Steps in hypothesis testing using the Chi-Squared Test
    1️⃣ State the null and alternative hypotheses
    2️⃣ Calculate the Chi-Squared statistic
    3️⃣ Determine the degrees of freedom
    4️⃣ Find the critical value
    5️⃣ Compare the calculated statistic to the critical value
  • In the expected value formula, TOTO represents the total observed count
  • What is the expected value for white flowers in the example if the total observed is 120, the total expected for white is 60, and the grand total is 240?
    30
  • The significance level represents the risk of making a Type I error