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Performing Hypothesis Tests: Means quiz

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  • What is the null hypothesis (H0) in a hypothesis test for means?
    The null hypothesis states that the population mean equals a specific value, such as H0: μ = 25,000.
  • When should you use a z-test instead of a t-test in hypothesis testing for means?
    A z-test is used when the population standard deviation (σ) is known; a t-test is used when σ is unknown.
  • What does the alternative hypothesis (Ha) represent in a hypothesis test?
    The alternative hypothesis suggests a different claim about the population mean, such as Ha: μ < 25,000.
  • How do you calculate the test statistic for a z-test?
    The z-test statistic is calculated as (sample mean - population mean) divided by (σ / sqrt(n)).
  • What is the formula for the t-test statistic when σ is unknown?
    The t-test statistic is (sample mean - population mean) divided by (s / sqrt(n)), where s is the sample standard deviation.
  • What is the significance level (alpha) in hypothesis testing?
    Alpha (α) is the threshold probability for rejecting the null hypothesis, commonly set at 0.05 or 0.1.
  • What does the p-value represent in hypothesis testing?
    The p-value is the probability of observing the sample data, or more extreme, assuming the null hypothesis is true.
  • What is the decision rule for rejecting the null hypothesis based on the p-value?
    If the p-value is less than alpha, we reject the null hypothesis; otherwise, we fail to reject it.
  • What are the criteria for using a z-test or t-test for means?
    You need a random sample and either a normal distribution or a sample size greater than 30.
  • How do you determine the direction of the test (left, right, or two-tailed)?
    The direction depends on the alternative hypothesis: '<' for left-tailed, '>' for right-tailed, and '≠' for two-tailed.
  • What is the role of degrees of freedom in a t-test?
    Degrees of freedom for a t-test is n - 1, where n is the sample size, and it is used to find the p-value.
  • How do you use a TI-84 calculator to perform a z-test for means?
    Select the Z-Test function, input the population mean, σ, sample mean, sample size, and choose the correct alternative hypothesis.
  • What information do you need to perform a t-test on a TI-84 calculator?
    You need the sample mean, sample standard deviation, sample size, and the hypothesized population mean.
  • What does it mean if the p-value is greater than alpha in a hypothesis test?
    If p-value > alpha, we fail to reject the null hypothesis, indicating insufficient evidence for the alternative hypothesis.
  • Why is it important to check if the sample is random and the distribution is normal or n > 30?
    These conditions ensure the validity of the hypothesis test and allow the use of z or t distributions.