458 Chapter 9 Hypothesis Testing Answers to Check Your Understanding Exercises for Section 9.4 1. a. H0: p = 0.15, H1: p ≠ 0.15 b. z = 1.98 c. P = 0.0478 Tech: 0.0477 d. We conclude that the proportion of students who read a newspaper differs from 0.15. 2. a. H0: p = 0.6, H1: p < 0.6 b. 150 c. 0.48 d. −3.00 e. Yes f. Yes 3. a. H0: p = 0.75, H1: p > 0.75 b. 1225 c. 0.7559183673 d. 0.4783759373 e. No f. No 4. a. H0: p = 0.80, H1: p < 0.80 b. z = −2.37 c. −1.645 d. We conclude that less than 80% of U.S. adults enjoy competing with others. SECTION 9.5 Hypothesis Tests for a Standard Deviation Objectives 1. Find critical values of the chi-square distribution 2. Test hypotheses about the standard deviation of a normal distribution Objective 1 Find critical values of the chi-square distribution The chi-square distribution was introduced in Section 8.4. The critical value ��2 �� represents the value that has area �� to its right. We review the method for finding critical values for the chi-square distribution from Table A.4. EXAMPLE 9.21 Find a critical value CAUTION The methods of this section apply only for samples drawn from a normal distribution. If the distribution differs even slightly from normal, these methods should not be used. Find the critical value ��2 0.05 for a chi-square distribution with 10 degrees of freedom. Solution We consult Table A.4. The critical value is located at the intersection of the row corresponding to 10 degrees of freedom and the column corresponding to �� = 0.05. The critical value is ��2 0.05 = 18.307. Degrees of Area in Right Tail Freedom 0.995 0.99 0.975 0.95 0.90 0.10 0.05 0.025 0.01 0.005 ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ 8 1.344 1.646 2.180 2.733 3.490 13.362 15.507 17.535 20.090 21.955 9 1.735 2.088 2.700 3.325 4.168 14.684 16.919 19.023 21.666 23.589 10 2.156 2.558 3.247 3.940 4.865 15.987 18.307 20.483 23.209 25.188 11 2.603 3.053 3.816 4.575 5.578 17.275 19.675 21.920 24.725 26.757 12 3.074 3.571 4.404 5.226 6.304 18.549 21.026 23.337 26.217 28.300 ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ Objective 2 Test hypotheses about the standard deviation of a normal distribution Hypothesis Tests for the Standard Deviation The null hypothesis for a standard deviation �� is of the form H0 : �� = ��0. The test is based on the fact that if H0 is true, then the test statistic ��2 = (n − 1) ⋅ s2 ��2 0 has a chi-square distribution with n − 1 degrees of freedom. We will focus on how to perform a test using the critical value method and Table A.4.
navidi_monk_elementary_statistics_2e_ch7-9
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