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11.15: Chapter Solution (Practice + Homework)

  • Page ID
    14741
  • 1.

    mean = 25 and standard deviation = 7.0711

    3.

    when the number of degrees of freedom is greater than 90

    5.

    \(df = 2\)

    6.

    a test of a single variance

    8.

    a left-tailed test

    10.

    \(H_0: \sigma^2 = 0.812\);

    \(H_a: \sigma^2 > 0.812\).

    12.

    a test of a single variance

    16.

    a goodness-of-fit test

    18.

    3

    20.

    2.04

    21.

    We decline to reject the null hypothesis. There is not enough evidence to suggest that the observed test scores are significantly different from the expected test scores.

    23.

    \(H_0\): the distribution of AIDS cases follows the ethnicities of the general population of Santa Clara County.

    25.

    right-tailed

    27.

    2016.136

    28.

    • 30.

      a test of independence

      a test of independence

      34.

      8

      36.

      6.6

      39.

      Smoking level per dayAfrican AmericanNative HawaiianLatinoJapanese AmericansWhiteTotals
      1-109,8862,74512,8318,3787,65041,490
      11-206,5143,0624,93210,6809,87735,065
      21-301,6711,4191,4064,7156,06215,273
      31+7597888002,3053,9708,622
      Totals18,8308,01419,96926,07827,55910,0450
      Table \(\PageIndex{54}\)

      41.

      Smoking level per dayAfrican AmericanNative HawaiianLatinoJapanese AmericansWhite
      1-107777.573310.118248.0210771.2911383.01
      11-206573.162797.526970.769103.299620.27
      21-302863.021218.493036.203965.054190.23
      31+1616.25687.871714.012238.372365.49
      Table \(\PageIndex{55}\)

      43.

      10,301.8

      44.

      right

      46.

      1. 48.

        test for homogeneity

        test for homogeneity

        52.

        All values in the table must be greater than or equal to five.

        54.

        3

        57.

        a goodness-of-fit test

        59.

        a test for independence

        61.

        Answers will vary. Sample answer: Tests of independence and tests for homogeneity both calculate the test statistic the same way \(\sum_{(i j)} \frac{(O-E)^{2}}{E}\). In addition, all values must be greater than or equal to five.

        63.

        true

        65.

        false

        67.

        225

        69.

        \(H_0: \sigma^2 \leq 150\)

        71.

        36

        72.

        Check student’s solution.

        74.

        The claim is that the variance is no more than 150 minutes.

        76.

        a Student's \(t\)- or normal distribution

        78.

        1. 80.
          1. 82.
            1. 84.
              1. 87.
                Marital statusPercentExpected frequency
                Never married31.3125.2
                Married56.1224.4
                Widowed2.510
                Divorced/Separated10.140.4
                Table \(\PageIndex{56}\)
                1. 89.
                  1. 91.
                    1. 94.

                      true

                      false

                      98.

                      1. 100.
                        1. 102.
                          1. 104.
                            1. 106.
                              1. 108.

                                true

                                true

                                112.

                                1. 114.
                                  1. 116.
                                    1. 118.
                                      1. 120.
                                        1. 122.
                                          1. The test statistic is always positive and if the expected and observed values are not close together, the test statistic is large and the null hypothesis will be rejected.
                                          2. Testing to see if the data fits the distribution “too well” or is too perfect.
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