Which best describes the p-value?

Answer: P(chi-square = 9.21 | df=4) The p-value for a chi-square test is the probability of observing a chi-square statistic at least as extreme (i.e., as large or larger) as the observed value, under the null hypothesis.

What is the correct conclusion?

Answer: Reject H0; there is significant evidence of an association Since p-value (0.024) < alpha (0.05), reject H0. There is significant evidence of an association between the two variables.

At alpha = 0.05, conclusion?

Answer: Fail to reject H0; insufficient evidence of association Since p = 0.078 alpha = 0.05, fail to reject H0. There is insufficient evidence of association.

AP Statistics · Topic 8.6

Carrying Out a Chi-Square Test for Homogeneity or Independence Practice

Q: At alpha = 0.05, conclusion?

Answer: Fail to reject H0; insufficient evidence of association Since p = 0.078 alpha = 0.05, fail to reject H0. There is insufficient evidence of association.

Part of Inference for Categorical Data: Chi-Square.(VAR-8.E)

Practice questions

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Sample questions

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Sample 1difficulty 2/5
$A chi-square test of independence yields chi-square = 9.21 with 4 degrees of freedom.$
$Which best describes the p-value?$
- A
  $P(chi-square >= 9.21 | df=4)$
  check_circle
- B
  $P(chi-square <= 9.21 | df=4)$
- C
  $P(chi-square = 9.21 | df=4)$
- D
  $P(chi-square > 9.21 | df=5)$
Why
$The p-value for a chi-square test is the probability of observing a chi-square statistic at least as extreme (i.e., as large or larger) as the observed value, under the null hypothesis.$
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Sample 2difficulty 2/5
$A chi-square test of independence with df = 6 produces chi-square = 14.5 and p-value = 0.024. Use alpha = 0.05.$
$What is the correct conclusion?$
- A
  $Reject H0; there is significant evidence of an association$
  check_circle
- B
  $Accept H0; the variables are independent$
- C
  $Reject H0; the variables are independent$
- D
  $Fail to reject H0; no evidence of association$
Why
$Since p-value (0.024) < alpha (0.05), reject H0. There is significant evidence of an association between the two variables.$
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Sample 3difficulty 2/5
$Software reports: chi-square = 8.40, df = 4, p = 0.078.$
$At alpha = 0.05, conclusion?$
- A
  $Fail to reject H0; insufficient evidence of association$
  check_circle
- B
  $Reject H0$
- C
  $p too low to interpret$
- D
  $Accept H0$
Why
$Since p = 0.078 > alpha = 0.05, fail to reject H0. There is insufficient evidence of association.$
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Sample 4difficulty 3/5
$A complete report includes$
- A
  $Just the conclusion$
- B
  $Test name, hypotheses, conditions, χ², df, p-value, and conclusion in context$
  check_circle
- C
  $Just χ²$
- D
  $Just the p-value$
Why
$Full inference report is required.$
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Sample 5difficulty 3/5
$A chi-square test of independence between music preference and age yields p = 0.31.$
$What is the appropriate conclusion?$
- A
  $p is too small to conclude anything$
- B
  $Insufficient evidence to conclude music preference and age are associated$
  check_circle
- C
  $Music preference and age are independent$
- D
  $Reject the null hypothesis$
Why
$With p = 0.31 > 0.05, fail to reject H0. We cannot conclude there is an association; this does NOT prove independence.$
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