2.5.3 Hypothesis testing for the normal distribution

    Cards (33)

    • What does the null hypothesis state in hypothesis testing?
      No significant difference
    • The alternative hypothesis contradicts the null hypothesis.
    • What type of error is committed when rejecting a true null hypothesis?
      Type I error
    • Common values for the significance level include 0.05, 0.01, and 0.10
    • Lower significance levels are used when falsely rejecting the null hypothesis has serious repercussions.
    • Match the significance level with its Type I error probability:
      0.05 (5%) ↔️ 5%
      0.01 (1%) ↔️ 1%
      0.10 (10%) ↔️ 10%
    • What is the definition of a Type I error in hypothesis testing?
      Rejecting a true null hypothesis
    • The choice of significance level depends on the consequences of a Type I error
    • What is the formula for calculating the test statistic in a normal distribution hypothesis test?
      z = \frac{\bar{x} - μ}{\frac{σ}{\sqrt{n}}}</latex>
    • In the test statistic formula, σσ represents the population standard deviation.
    • What is the first step in determining the critical region in hypothesis testing?
      Identify the significance level
    • The critical region is the set of values for the test statistic that lead to rejecting the null hypothesis
    • In hypothesis testing, μμ represents the population mean stated in the null hypothesis.
    • σσ is the sample standard deviation.

      False
    • In an example, we have a sample of 36 apples with a mean weight of 105g</latex>. The null hypothesis states that the population mean weight is 100g100g. The population standard deviation is 10g10g. Using the formula, the calculated z-value is approximately 3.00.
    • Steps to determine the critical region in hypothesis testing
      1️⃣ Identify the significance level (α)(α).
      2️⃣ Determine if the test is one-tailed or two-tailed.
      3️⃣ Use standard normal distribution tables to find the critical value(s) corresponding to (α)(α).
    • Match the significance level with its critical value for a one-tailed test:
      0.05 ↔️ 1.645
      0.01 ↔️ 2.33
      0.10 ↔️ 1.28
    • The null hypothesis states that there is a significant difference or effect.
      False
    • A Type I error occurs when we reject a true null hypothesis.
    • What is the formula for calculating the test statistic in a normal distribution?
      z = \frac{\bar{x} - μ}{\frac{σ}{\sqrt{n}}}</latex>
    • If the calculated z-value is 3.00, it is greater than the critical value for a one-tailed test with α=α =0.05 0.05.
    • For a one-tailed test with α=α =0.05 0.05, the critical value is 1.645.
    • In hypothesis testing, we can reject the null hypothesis if the test statistic falls within the critical region.
    • What should you use to find critical values for hypothesis testing?
      Standard normal distribution tables
    • The critical value for a one-tailed test with α=α =0.05 0.05 is 1.645
    • The critical value for a two-tailed test with α=α =0.01 0.01 is ±2.58.
    • What is the critical value for a one-tailed test with α=α =0.10 0.10?

      1.28
    • Steps to make a decision in hypothesis testing
      1️⃣ Compare the test statistic to the critical value
      2️⃣ Compare the p-value to α
      3️⃣ Reject H0 if the test statistic is more extreme or the p-value is less than α
      4️⃣ Fail to reject H0 otherwise
    • What should you do if the test statistic is more extreme than the critical value?
      Reject H0
    • If the p-value is greater than α, you should reject H0.
      False
    • For a p-value less than α, you should reject H0.
    • What does it mean if you reject H0?
      Significant evidence supports H1
    • If you fail to reject H0, it means there is enough evidence to support H1.
      False