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Two Means - Known Variance quiz

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  • What type of test is used for comparing two means when population standard deviations are known?
    A z-test is used instead of a t-test when population standard deviations are known.
  • What is the formula for the z-score in a two means test with known variances?
    The formula is z = (μ1 - μ2) / sqrt(σ1^2/n1 + σ2^2/n2).
  • What is the null hypothesis when testing two means with known variances?
    The null hypothesis is that the two means are equal, or μ1 = μ2.
  • How do you determine the alternative hypothesis in a two means test?
    The alternative hypothesis is based on the claim being tested, such as μ1 < μ2 if testing whether one mean is less than the other.
  • What values are substituted in the denominator of the z-score formula when population standard deviations are known?
    Population standard deviations (σ1 and σ2) are used instead of sample standard deviations.
  • What is the next step after calculating the z-score in a two means hypothesis test?
    The next step is to convert the z-score into a p-value.
  • How do you interpret the p-value in relation to the alpha level in hypothesis testing?
    If the p-value is less than the alpha level, you reject the null hypothesis.
  • What does rejecting the null hypothesis indicate in the context of two means testing?
    It indicates there is enough evidence to support the alternative hypothesis, such as one mean being less than the other.
  • What conditions must be met for valid inference in a two means test with known variances?
    Samples must be independent and random, and either the data must be normal or sample sizes must be greater than 30.
  • What technology can be used to perform a two means z-test calculation?
    A TI-84 calculator can be used, specifically the '2-SampZTest' function.
  • What information must be entered into technology for a two means z-test?
    You must enter the population standard deviations, sample means, and sample sizes for both groups.
  • How do you find the p-value for a left-tailed test in a two means z-test?
    Find the area to the left of the calculated z-score using a z-table or technology.
  • What sample sizes are considered sufficient for the normality condition in a two means z-test?
    Sample sizes greater than 30 are considered sufficient for the normality condition.
  • What is the conclusion if the p-value is much smaller than the alpha level?
    You reject the null hypothesis and conclude there is evidence for the alternative hypothesis.
  • What is the practical interpretation of rejecting the null hypothesis in the grocery checkout example?
    It means there is enough evidence to suggest self checkout lanes have shorter times than cashier lanes.