What is the t test statistic?

Answer: 2.77 t = 3.5/(4.0/sqrt(10)) = 3.5/1.265 = 2.77.

Using d = before - after, what is the mean difference?

Answer: 2.8 Differences: 2, 4, -2, 5, 5. Mean = (2+4-2+5+5)/5 = 14/5 = 2.8.

What is the two-sided p-value?

Answer: 0.078 For a two-sided test, p = 2 (one-tailed area) = 2 0.039 = 0.078.

AP Statistics · Topic 7.5

Carrying Out a Test for a Population Mean Practice

Part of Inference for Quantitative Data: Means.(VAR-7.B)

Practice questions

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Sample questions

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Sample 1difficulty 1/5
$For 10 paired differences, x-bar_d = 3.5, s_d = 4.0. Test H0: mu_d = 0 vs Ha: mu_d > 0.$
$What is the t test statistic?$
- A
  $2.77$
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- B
  $1.39$
- C
  $0.875$
- D
  $8.75$
Why
$t = 3.5/(4.0/sqrt(10)) = 3.5/1.265 = 2.77.$
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Sample 2difficulty 1/5
$Five subjects' before/after weights (lb): (180,178), (200,196), (165,167), (210,205), (175,170).$
$Using d = before - after, what is the mean difference?$
- A
  $1.5$
- B
  $5.0$
- C
  $-2.8$
- D
  $2.8$
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Why
$Differences: 2, 4, -2, 5, 5. Mean = (2+4-2+5+5)/5 = 14/5 = 2.8.$
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Sample 3difficulty 1/5
$A two-sided t-test of H0: mu = 0 yields t = 1.85 with df = 20. The one-tailed area is 0.039.$
$What is the two-sided p-value?$
- A
  $0.039$
- B
  $0.078$
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- C
  $0.961$
- D
  $0.020$
Why
$For a two-sided test, p = 2 * (one-tailed area) = 2 * 0.039 = 0.078.$
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Sample 4difficulty 1/5
$A random sample of 36 bags has a mean weight of 49.4 lb with s = 1.8 lb. Test H0: mu = 50 vs Ha: mu < 50.$
$What is the value of the t test statistic?$
- A
  $-0.33$
- B
  $-2.00$
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- C
  $-3.33$
- D
  $-0.60$
Why
$t = (49.4 - 50)/(1.8/sqrt(36)) = -0.6/0.30 = -2.00.$
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Sample 5difficulty 2/5
$A test fails to reject H0: mu = 50.$
$The most appropriate conclusion is:$
- A
  $mu is exactly 50.$
- B
  $There is insufficient evidence to conclude mu differs from 50.$
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- C
  $There is strong evidence mu = 50.$
- D
  $The test must be repeated.$
Why
$Failing to reject H0 does not prove H0; it indicates lack of sufficient evidence against it.$
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