Sample Tests for a Population Mean

This section talks about using the central limit theorem to test a population mean when the sample size is large. It also addresses how to interpret the test results in the application background. Then, it discusses testing a population mean when the sample size is small, outlines a five-step testing procedure, and illustrates the procedure with an example. Study the example carefully and complete the relevant exercises and applications. Finally, it talks about large sample tests for a population proportion. The critical value and p-value approach are introduced based on a standardized test statistic.

Small Sample Tests for a Population Mean

Answers

1. a. Z \leq-1.645
    b. T \leq-2.571 or T \geq 2.571
    c. T \geq 1.319
    d. Z \leq-1645 or Z \geq 1.645

3. a. T \leq-0.855
    b. Z \leq-1.645
    c. T \leq-2.201 or T \geq 2.201
    d. T \geq 3.435

5. a. T=-2.690, d f=19,-t_{0.005}=-2.861, do not reject H_{0}.
    b. 0.01 < p-value < 0.02, \alpha=0.01, do not reject H_{0}.

7. a. T=2.398, d f=7, t_{0.05}=1.895, reject H_{0}.
    b. 0.01 < p-value < 0.025, \alpha=0.05, reject H_{0}

9. T=-7.560, d f=12,-t_{0.10}=-1.356, reject H_{0}.

11. T=-7.076, d f=5,-t_{0.0005}=-6.869, reject H_{0}

13. a. T=-1.483, d f=14,-t_{0.05}=-1.761, do not reject H_{0};
      b. T=-1.483, d f=14,-t_{0.10}=-1.345, reject H_{0};

15. a. T=2.069, d f=6, t_{0.10}=1.44, reject H_{0};
      b. T=2.069, d f=6, t_{0.05}=1.943, reject H_{0}.

17. T=4.472, d f=4, t_{0.10}=1.533, reject H_{0}.

19. T=0.798, d f=24, t_{0.10}=1.318, do not reject H_{0}

21. a. T=-1.773, d f=4,-t_{0.05}=-2.132, do not reject H_{0}.
      b. 0.05 < p-value < 0.10
      c. \alpha=0.05, do not reject \mathrm{H}_{0}