Chi-Square Test for Election Survey

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to Lesson

Podcast

Play an AI-generated podcast conversation about this lesson
Download our mobile app to listen on the go
Get App

Questions and Answers

In the provided Chi-Square test, what is the null hypothesis?

  • Voter preferences have not changed since the last election. (correct)
  • Voter preferences have changed since the last election.
  • The sample size is too small to draw any conclusions.
  • At least one proportion is not equal to its specified value.

What is the alternative hypothesis for the given Chi-Square test?

  • Voter preferences for party B have significantly increased.
  • Voter preferences have not changed since the last election.
  • $H_a$: All voter preferences are equal.
  • At least one proportion is not equal to its specified value. (correct)

Based on the information provided, what is the expected frequency for party A?

  • 408
  • 372 (correct)
  • 362
  • 310

What is the expected frequency for party B according to the chi-square test?

<p>612 (A)</p> Signup and view all the answers

What is the expected frequency for party C in the Chi-Square test?

<p>216 (A)</p> Signup and view all the answers

Given the Chi-Square test result of 6.34634, what is the correct interpretation of this value?

<p>The measure of how different the observed voter distribution is from expected if preferences haven’t changed. (D)</p> Signup and view all the answers

For this Chi-Square test, what are the degrees of freedom (DF)?

<p>2 (B)</p> Signup and view all the answers

Based on the Chi-Square test results (test statistic = 6.34634, p-value = 0.042, significance level = 0.05), what is the correct statistical conclusion?

<p>Reject $H_0$; there is enough statistical evidence to show that voter preferences have changed (for the population). (A)</p> Signup and view all the answers

Flashcards

Null Hypothesis

The null hypothesis states there is no change in voter preferences; the proportions are the same as the last election.

Alternative Hypothesis

The alternative hypothesis states that at least one voter preference proportion is different from the last election.

Expected Frequency

Expected frequency is calculated by multiplying the sample size by the hypothesized proportion for each category.

Expected Frequency for Party A

For Party A: 1200 * 0.31 = 372

Signup and view all the flashcards

Expected Frequency for Party B

For Party B: 1200 * 0.51 = 612

Signup and view all the flashcards

Expected Frequency for Party C

For Party C: 1200 * 0.18 = 216

Signup and view all the flashcards

Computed Test Statistic

The calculated Chi-Square test statistic is 6.346 (rounded to 3 decimal places).

Signup and view all the flashcards

Degrees of Freedom

With 3 categories, the degrees of freedom (DF) is 2 (number of categories minus 1).

Signup and view all the flashcards

Study Notes

  • An election was held last year with three parties: A, B, and C.
  • Party A received 31% of the vote.
  • Party B received 51% of the vote.
  • Party C received 18% of the vote.
  • A survey of 1,200 voters was conducted to determine the party they would vote for in the next election.
  • A test is being conducted to determine if voter support has changed since the last election, using a 5% significance level.

Observed vs Expected

  • Observed frequency for party A is 408.
  • Observed frequency for party B is 571.
  • Observed frequency for party C is 221.

Null Hypothesis

  • Voter preferences have not changed since the last election.

Alternative Hypothesis

  • At least one proportion is not equal to its specified value.

Expected Frequencies

  • To calculate the expected frequency for each party, multiply the total survey size (1200) by the party's proportion from the last election.
  • Expected frequency for party A: 1200 * 0.31 = 372
  • Expected frequency for party B: 1200 * 0.51 = 612
  • Expected frequency for party C: 1200 * 0.18 = 216

Chi-Square Test Statistic

  • Computed test statistic is 6.346 (rounded to three decimal places).

Degrees of Freedom

  • The degrees of freedom (DF) for this test are 2.

Table Test Statistic

  • The table test statistic value is required for comparison with the computed test statistic, but not provided.

Statistical Conclusion

  • Reject the null hypothesis if the computed test statistic exceeds the critical value from the chi-square distribution with 2 degrees of freedom at a 5% significance level.
  • If the null hypothesis is rejected, there is enough statistical evidence to suggest that voter preferences have changed (for the population).
  • If the null hypothesis is not rejected, there is not enough statistical evidence to suggest that voter preferences have changed (for the population).

Required Condition

  • The rule of 5 requires the expected frequency for each category to be 5 or more.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Quiz Team

More Like This

Use Quizgecko on...
Browser
Open
Browser
Browser