AP Statistics · Topic 7.4

Setting Up a Test for a Population Mean Practice

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

Practice questions

8

Want a predicted score for the whole AP STAT exam? Take the 20-question diagnostic and Lumi will plan the rest.

Sample questions

5 of 8 — sign in to practice the rest with adaptive difficulty and mastery tracking.

  1. Sample 1difficulty 1/5

    A coach claims a new training method reduces 5K times.

    Pair index Difference 0

    Using d = before - after, the appropriate alternative for "training reduces times" is:

    • A

      Ha: mu_d = 0

    • B

      Ha: mu_d != 0

    • C

      Ha: mu_d > 0

      check_circle
    • D

      Ha: mu_d < 0

    Why

    If training reduces times, after < before, so before - after > 0; thus Ha: mu_d > 0.

  2. Sample 2difficulty 2/5

    A car maker claims average mileage is at least 35 mpg. Consumer testing yields x-bar = 33.8 with t = -1.40.

    0 t upper-tail p-value

    Using Ha: mu < 35 with df = 24, the p-value is roughly:

    • A

      0.50

    • B

      0.087

      check_circle
    • C

      0.913

    • D

      0.005

    Why

    For df = 24 and t = -1.40, the lower-tail p-value is about 0.087.

  3. Sample 3difficulty 2/5

    A two-sided t-test at alpha = 0.05 with df = 18 has critical values ±2.101.

    -2.101 2.101 df=18, alpha=0.05

    Which observed t leads to rejection of H0?

    • A

      t = 1.90

    • B

      t = 0.00

    • C

      t = 2.50

      check_circle
    • D

      t = -1.50

    Why

    Reject when |t| > 2.101. Only t = 2.50 satisfies this.

  4. Sample 4difficulty 2/5

    A two-sided t-test gives p = 0.06.

    0 two-sided test

    A one-sided test in the observed direction would have a p-value of:

    • A

      0.94

    • B

      0.06

    • C

      0.12

    • D

      0.03

      check_circle

    Why

    For a symmetric distribution, the one-sided p in the observed direction is half the two-sided p: 0.06/2 = 0.03.

  5. Sample 5difficulty 3/5

    For the same data and direction-matching alternative, one-tailed p-value vs two-tailed

    • A

      Equal

    • B

      One-tailed = (two-tailed)/2

      check_circle
    • C

      Two-tailed = one-tailed/2

    • D

      Independent

    Why

    For symmetric distributions, halving the two-tailed p-value gives one-tailed.