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Two Means - Unknown, Equal Variance quiz

컨트롤 버튼이 '내비게이션' 모드로 변경되었습니다.
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  • What assumption allows us to use the pooled standard deviation in a two means hypothesis test?
    We assume that the two populations have equal variances, which allows us to use the pooled standard deviation.
  • How is the pooled standard deviation calculated?
    It is calculated as a weighted average of the two sample variances, providing a better approximation for the population standard deviation.
  • What is the null hypothesis when testing two means with equal variances?
    The null hypothesis is that the two population means are equal, or mu1 = mu2.
  • What is the alternative hypothesis if you want to test if a new method improves scores?
    The alternative hypothesis is that the mean of the old method is less than the mean of the new method, or mu1 < mu2.
  • What information do you need from each sample to perform the test?
    You need the sample mean, sample standard deviation, and sample size from each group.
  • What changes in the t-score formula when using pooled standard deviation?
    The denominator uses the pooled standard deviation instead of the individual sample standard deviations.
  • How do you find the degrees of freedom for this test?
    Add the sample sizes of both groups, subtract one from each, and sum the results: (n1 - 1) + (n2 - 1).
  • What is the next step after calculating the t-score?
    Turn the t-score into a p-value using a t-table or calculator.
  • How do you determine whether to reject the null hypothesis?
    Compare the p-value to the significance level (alpha); if the p-value is less than alpha, reject the null hypothesis.
  • What does rejecting the null hypothesis indicate in this context?
    It indicates there is enough evidence to support the alternative hypothesis, such as improved test scores with the new method.
  • What sample size condition must be met for valid results?
    Each sample size should be greater than 30 to satisfy normality assumptions.
  • What type of samples are required for this test?
    Independent random samples are required.
  • What is the significance level (alpha) used in the example?
    The significance level used is 0.05.
  • What was the calculated t value in the example provided?
    The t value calculated was approximately -5.43.
  • What was the p-value obtained in the example, and what does it mean?
    The p-value was approximately 2.05 x 10^-7, which is much less than alpha, so the null hypothesis is rejected.