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Two Means - Unknown, Unequal Variance quiz

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  • What is the null hypothesis when testing two means with unknown, unequal variances?
    The null hypothesis is that the two population means are equal (μ1 = μ2), or equivalently, that their difference is zero (μ1 - μ2 = 0).
  • How is the alternative hypothesis typically written in a two-sample test of means?
    The alternative hypothesis is usually that the means are not equal (μ1 ≠ μ2), indicating a two-tailed test.
  • What conditions must be checked before performing a two-sample t-test with unknown, unequal variances?
    You must check that the samples are random and independent, and that the populations are normally distributed or the sample sizes are large.
  • What is the formula for the test statistic in a two-sample t-test with unknown, unequal variances?
    The test statistic is (x̄1 - x̄2) - (μ1 - μ2) divided by the square root of (s1²/n1 + s2²/n2), where s1 and s2 are sample standard deviations.
  • How do you determine the degrees of freedom for the t-distribution in this test?
    A common method is to use the smaller sample size minus one (min(n1, n2) - 1) for the degrees of freedom.
  • What is the point estimator for the difference in means in a confidence interval?
    The point estimator is the difference between the sample means, x̄1 - x̄2.
  • How is the margin of error calculated for a confidence interval of two means?
    The margin of error is the critical t-value times the square root of (s1²/n1 + s2²/n2).
  • What does it mean if the confidence interval for the difference in means does not include zero?
    It means there is enough evidence to reject the null hypothesis and conclude a significant difference between the means.
  • What is the conclusion if the p-value is less than the significance level (alpha) in a two-sample t-test?
    If p < alpha, you reject the null hypothesis and conclude there is a significant difference between the means.
  • How do you use a TI-84 calculator to perform a two-sample t-test with statistics?
    Enter the sample means, standard deviations, and sizes, select the correct alternative hypothesis, set pooled to 'no', and calculate the p-value.
  • What is the rule for interpreting a confidence interval regarding the null hypothesis?
    If the interval includes zero, you fail to reject the null hypothesis; if it does not include zero, you reject the null hypothesis.
  • How do you construct the upper and lower bounds of a confidence interval for two means?
    Add and subtract the margin of error from the point estimator to get the upper and lower bounds.
  • What does 'pooled' mean in the context of a two-sample t-test, and what should you select when variances are unequal?
    Pooled refers to assuming equal variances; when variances are unequal, you should select 'no' for pooled.
  • What is the significance of the sample standard deviations in the test statistic formula?
    Sample standard deviations (s1 and s2) are used because population standard deviations are unknown and assumed unequal.
  • How do you interpret a confidence interval that ranges from negative to positive values and includes zero?
    If the interval includes zero, it suggests there is not enough evidence to claim a difference between the two means.