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Two Means - Sigma Known Hypothesis Test - Excel quiz

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  • When are you required to use a z-test instead of a t-test for comparing two means?
    You use a z-test when the population standard deviations (sigma1 and sigma2) are known.
  • What is the null hypothesis (H₀) when testing two means?
    The null hypothesis is that the two population means are equal (μ₁ = μ₂).
  • How do you express the alternative hypothesis if you suspect mean 1 is less than mean 2?
    The alternative hypothesis is μ₁ < μ₂.
  • What formula is used to calculate the z-score for two means with known sigmas?
    The formula is z = (x̄₁ - x̄₂) / sqrt(σ₁²/n₁ + σ₂²/n₂).
  • Which Excel function is used to calculate the sample mean from data?
    The function is =AVERAGE(range).
  • How do you calculate the numerator for the z-score in Excel?
    Subtract the second sample mean from the first: x̄₁ - x̄₂.
  • How do you calculate σ₁²/n₁ in Excel?
    Square sigma1, then divide by n1: =sigma1^2/n1.
  • Which Excel function is used to find the cumulative left-tail probability for a z-score?
    Use =NORM.S.DIST(z, TRUE).
  • What does the p-value represent in hypothesis testing?
    The p-value is the probability of observing a test statistic as extreme as, or more extreme than, the one calculated, assuming the null hypothesis is true.
  • What decision do you make if the p-value is less than alpha?
    You reject the null hypothesis.
  • In the example, what were the sample sizes for both groups?
    Both sample sizes were 30 (n₁ = 30, n₂ = 30).
  • What were the values of sigma1 and sigma2 in the example?
    Sigma1 was 9.73 and sigma2 was 5.91.
  • If your alternative hypothesis uses a less than symbol, which tail probability do you use?
    You use the left-tail probability.
  • What conclusion was reached in the example when the p-value was 0.04 and alpha was 0.05?
    The null hypothesis was rejected, indicating enough evidence that machine A produces less on average than machine B.
  • Why is it helpful to break the z-score formula into parts when calculating in Excel?
    Breaking the formula into parts reduces the chance of making calculation errors and makes the process easier.