At alpha = 0.05, what conclusion?

Answer: Reject H0; data inconsistent with claimed distribution Since p = 0.048 < 0.05, reject H0. There is evidence the observed counts are inconsistent with the hypothesized distribution.

What is the correct conclusion?

Answer: Fail to reject H0; insufficient evidence to conclude observed counts differ from claimed distribution Since p-value (0.231) alpha (0.05), fail to reject H0. There is not enough evidence to conclude the observed counts differ from the hypothesized distribution.

χ² is a sum of contributions, each ≥ 0. So χ² is

Answer: Always ≥ 0 Each (O−E)²/E ≥ 0; their sum cannot be negative.

AP Statistics · Topic 8.3

Carrying Out a Chi-Square Test for Goodness of Fit Practice

Q: What is the correct conclusion?

Answer: Fail to reject H0; insufficient evidence to conclude observed counts differ from claimed distribution Since p-value (0.231) alpha (0.05), fail to reject H0. There is not enough evidence to conclude the observed counts differ from the hypothesized distribution.

Q: χ² is a sum of contributions, each ≥ 0. So χ² is

Answer: Always ≥ 0 Each (O−E)²/E ≥ 0; their sum cannot be negative.

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

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Sample questions

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Sample 1difficulty 2/5
$A chi-square goodness-of-fit on a six-category variable returns chi-square = 11.2 and p = 0.048.$
$At alpha = 0.05, what conclusion?$
- A
  $Reject H0; data inconsistent with claimed distribution$
  check_circle
- B
  $Fail to reject H0$
- C
  $Reject H0; data fit the distribution$
- D
  $Accept H0$
Why
$Since p = 0.048 < 0.05, reject H0. There is evidence the observed counts are inconsistent with the hypothesized distribution.$
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Sample 2difficulty 2/5
$A chi-square goodness-of-fit test yields chi-square = 5.6 with df = 4 and p-value = 0.231 at alpha = 0.05.$
$What is the correct conclusion?$
- A
  $Fail to reject H0; insufficient evidence to conclude observed counts differ from claimed distribution$
  check_circle
- B
  $Reject H0; the distribution matches$
- C
  $Reject H0; the distribution differs$
- D
  $Accept the alternative$
Why
$Since p-value (0.231) > alpha (0.05), fail to reject H0. There is not enough evidence to conclude the observed counts differ from the hypothesized distribution.$
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Sample 3difficulty 3/5
$χ² is a sum of contributions, each \geq 0. So χ² is$
- A
  $Always > 1$
- B
  $Always \geq 0$
  check_circle
- C
  $Either sign$
- D
  $Always negative$
Why
$Each (O-E)²/E \geq 0; their sum cannot be negative.$
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Sample 4difficulty 3/5
$χ² calculated = 7.81 with df=3 at α = 0.05 (critical = 7.81)$
- A
  $Insufficient information$
- B
  $Reject H₀ (just at the boundary)$
  check_circle
- C
  $Always reject$
- D
  $Always fail to reject$
Why
$Equality means p \approx α; conventionally treated as borderline reject.$
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Sample 5difficulty 3/5
$The χ² distribution is$
- A
  $Uniform$
- B
  $Bimodal$
- C
  $Skewed right (always non-negative)$
  check_circle
- D
  $Symmetric$
Why
$χ² is non-negative and right-skewed; it becomes more symmetric as df grows.$
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