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Two Means - Unknown, Equal Variance quiz

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  • What is the pooled standard deviation used for in hypothesis testing with two means?
    It is a weighted average of the two sample variances, used to improve the accuracy of the test when population variances are assumed equal.
  • When can you assume equal variances in a two-sample t-test?
    When the populations are similar enough that their variances can reasonably be considered the same.
  • What is the null hypothesis when testing two means with unknown but equal variances?
    The null hypothesis is that the two population means are equal (μ1 = μ2).
  • How do you calculate degrees of freedom for the pooled t-test?
    Add the sample sizes of both groups, subtract one from each, and then add those results together (n1-1) + (n2-1).
  • What is the formula for the test statistic in a pooled two-sample t-test?
    t = (μ1 - μ2) / sp * sqrt(1/n1 + 1/n2), where sp is the pooled standard deviation.
  • What is the main advantage of using the pooled standard deviation?
    It provides a better estimate of the population standard deviation, leading to more accurate hypothesis test results.
  • What must be true about the samples in a pooled two-sample t-test?
    The samples must be independent and randomly selected.
  • What is the alternative hypothesis if you want to test if one mean is less than the other?
    The alternative hypothesis is μ1 < μ2.
  • How do you decide whether to reject the null hypothesis in a pooled t-test?
    Compare the p-value to the significance level (alpha); if the p-value is less than alpha, reject the null hypothesis.
  • What sample size condition allows you to use the normal approximation in a pooled t-test?
    Each sample size should be greater than 30, or the data should be normally distributed.
  • What does a very small p-value indicate in the context of hypothesis testing?
    It suggests strong evidence against the null hypothesis, supporting the alternative hypothesis.
  • What information do you need from each sample to perform a pooled t-test?
    You need the sample mean, sample standard deviation, and sample size for each group.
  • What is the purpose of the pooled option on a calculator when performing a two-sample t-test?
    Selecting 'pooled' tells the calculator to assume equal variances and use the pooled standard deviation in calculations.
  • If the p-value is 2.05 x 10^-7 and alpha is 0.05, what is the conclusion?
    Reject the null hypothesis because the p-value is much smaller than alpha.
  • Why might professors allow technology use for pooled t-tests?
    Because the calculations for the pooled standard deviation and test statistic can be complex and time-consuming by hand.