STATS Quizzes: Hypothesis Testing
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Questions and Answers

In a hypothesis test, what does a smaller level of significance (alpha) imply?

  • A reduced probability of rejecting a false null hypothesis.
  • A larger critical region in the distribution.
  • A lower probability of rejecting a true null hypothesis. (correct)
  • A greater probability of rejecting a true null hypothesis.

A researcher is testing if the average height of students in two different universities are equal. Which type of hypothesis test is most appropriate?

  • Two-tailed z-test
  • One-tailed t-test
  • One-tailed z-test
  • Two-tailed t-test (correct)

What critical value of z should be used to construct a 95% confidence interval?

  • 1.645
  • 2.575
  • 2.33
  • 1.96 (correct)

In what situation is a paired t-test most suitable?

<p>Assessing the difference in means between two related samples. (D)</p> Signup and view all the answers

A researcher wants to determine if there is a significant difference in the proportion of males and females who prefer a certain brand of coffee. Which test is most appropriate?

<p>Chi-square test for independence (B)</p> Signup and view all the answers

What does the p-value represent in hypothesis testing?

<p>The probability of observing a test statistic as extreme as, or more extreme than, the one computed if the null hypothesis is true. (B)</p> Signup and view all the answers

A researcher is conducting a one-tailed hypothesis test with a significance level of 0.05. In which of the following scenarios would they reject the null hypothesis?

<p>p-value = 0.01 (A)</p> Signup and view all the answers

What happens to the critical value of a t-distribution as the degrees of freedom increase?

<p>It approaches the critical value of the standard normal distribution. (D)</p> Signup and view all the answers

In the context of hypothesis testing, what is a Type II error?

<p>Failing to reject a null hypothesis that is actually false. (B)</p> Signup and view all the answers

Which of the following is an assumption of the independent samples t-test?

<p>The data are normally distributed. (C)</p> Signup and view all the answers

Flashcards

One-tailed test

A statistical test where the critical area of a distribution is one-sided, meaning it tests if a sample is greater than or less than a certain range of values.

Two-tailed test

A statistical test in which the critical area of a distribution is two-sided and tests whether a sample is greater than or less than a certain range of values.

Level of significance (alpha)

The probability of rejecting the null hypothesis when it is actually true. Commonly set at 0.05 (5%) or 0.01 (1%).

T-value

A test statistic used for small sample sizes (typically n < 30) or when the population standard deviation is unknown. Measures the difference between sample and population means.

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Z-value

A test statistic used for large sample sizes (typically n ≥ 30) and when the population standard deviation is known. Measures how many standard deviations an element is from the mean.

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Study Notes

  • Summary of upcoming quizzes for STATS

QUIZ (TOM)

  • Consists of four tests

TEST I (1-10)

  • The scope includes items 1 through 10

TEST II (5 items + 5)

  • Contains five multiple-choice items
  • Includes +5 additional items
  • Focuses on identifying whether a test is two-tailed or one-tailed

TEST III (2 items)

  • Composed of two items
  • Requires determining the level of significance

TEST IV

  • Involves finding the T value
  • Involves finding the Z value

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Upcoming quizzes for STATS. The quizzes consist of four tests including items 1-10, identifying one-tailed vs. two-tailed tests, determining significance levels, and finding T and Z values.

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