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One of the more popular statistics reported in the media is the president's job approval rating. The approval rating is reported as the proportion of the population who approve of the job that the sitting president is doing and is typically based on a random sample of registered voters where the sample size is the same week to week. Complete parts (a) and (b) below. a) This proportion tends to fluctuate from week to week. Name some reasons for the fluctuation in the statistic. Select all valid reasons below. A. The proportion could be changing due to a large change in the composition of the population. Ly B. The proportion could be changing because people's attitudes are changing. Y C. The proportion could be changing due to sampling error; different people are in the sample. D. The proportion could be changing because the sampling size of the poll is changing b) A poll showed the approval rating to be 0.43 (43%). A second poll based on 2000 randomly selected voters showed that 878 approved of the job the president was doing. Do the results of the second poll indicate that the proportion of voters who approve of the job the president is doing is significantly higher than the original level? Explain. Assume the a = 0.05 level of significance Identify the null and alternative hypotheses for this test. O A. Ho: P #0.43 O B. Ho: P > 0.43 O C. Ho: P = 0.43 H1: p = 0.43 H1 : p = 0.43 H1: p 0.43 H1: p #0.43 Find the test statistic for this hypothesis test. z= (Round to two decimal places as needed.) Help Me Solve This View an Example Get More Help - Clear All Check Answer2 Test the hypothesis using the P-value approach. Be sure to verify the requirements of the test. Ho: p = 0.5 versus H1 : p > 0.5 = 250; x = 130, a = 0.05 . . . . Is npo (1 - Po) 2 10? O No Yes Use technology to find the P-value. P-value = (Round to three decimal places as needed.) Help Me Solve This View an Example Get More Help - Clear All Check Answer3 Several years ago, 45% of parents who had children in grades K-12 were satisfied with the quality of education the students receive. A recent poll asked 1,095 parents who have children in grades K-12 if they were satisfied with the quality of education the students receive. Of the 1,095 surveyed, 498 indicated that they were satisfied. Construct a 95% confidence interval to assess whether this represents evidence that parents' attitudes toward the quality of education have changed. What are the null and alternative hypotheses? Ho: p = 0.45 versus H1 : p # 0.45 (Round to two decimal places as needed. Use technology to find the 95% confidence interval. The lower bound is. The upper bound is Round to two decimal places as needed.) Help Me Solve This View an Example Get More Help - Clear All Check Answer4 In a survey, 31% of the respondents stated that they talk to their pets on the telephone. A veterinarian believed this result to be too high, so he randomly selected 220 pet owners and discovered that 63 of them spoke to their pet on the telephone. Does the veterinarian have a right to be skeptical? Use the a = 0.01 level of significance. Because npo (1 - Po) = V 10, the sample size is 5% of the population size, and the sample the requirements for testing the hypothesis satisfied. (Round to one decimal place as needed.) can be reasonably assumed to be random, n to be random, is given to not be random, cannot be reasonably assumed to be random, Help Me Solve This View an Example Get More Help - Clear All Check Answer5 In a previous year, 58% of females aged 15 and older lived alone. A sociologist tests whether this percentage is different today by conducting a random sample of 650 females aged 15 and older and finds that 382 are living alone. Is there sufficient evidence at the a = 0.05 level of significance to conclude the proportion has changed Because npo (1 - Po) = V 10, the sample size is 5% of the population size, and the sample a random sample, all of the requirements for testing the hypothesis satisfied. (Round to one decimal place Help Me Solve This View an Example Get More Help - Clear All Check Answer6 Complete parts (a) through (c) below. X (a) Determine the critical value(s) for a right-tailed test of a population mean at the a = 0.10 level of significance with 10 degrees of freedom. (b) Determine the critical value(s) for a left-tailed test of a population mean at the a = 0.01 level of significance based on a sample size of n = 15. t-Distribution Area in Right Tail (c) Determine the critical value(s) for a two-tailed test of a population mean at the a = 0.05 level of significance based on a sample size of n = 18. Click here to view the t-Distribution Area in Right Tail. t-Distribution (a) torit = (Round to three decimal places as needed.) Area in Right Tail df 0.25 0.15 0.10 0.05 0.025 0.02 0.01 0.005 0.0025 0.001 0.0005 df 1.000 1.376 1.963 3.078 6.314 12.70 15.894 31.821 63.657 127.321 18.309 636.61 0.816 1.061 1.386 2.920 4 203 4.849 6.965 9.925 14.089 22.327 31.599 0.765 0.978 1.250 2 353 3.482 4.541 5.841 7 453 10.215 12 924 0.741 0.941 1.190 1.533 2132 2.776 2 090 3.747 4.604 5 508 8.610 5 0.727 0.920 1.156 1.476 2.015 2.571 2.757 3.365 4.032 4.713 6.869 6 0.718 0.906 1.134 1.943 2.447 2.612 3.143 3.707 4.317 5.208 5.959 7 0.711 2.36 2.517 2.998 3.499 4.029 4.785 5.408 2.306 2.449 2.896 3.355 3.833 4.501 5.041 9 0.706 0.703 2.262 2.398 2.821 3.250 3.690 4 297 4.781 10 0.700 0.879 1.093 2.228 2.359 2.764 3.169 3.581 4.144 4.587 10 0.697 0.876 1.088 1.796 2.201 2.328 2.718 3.497 4.437 11 2.303 2.681 3.055 3.428 4.318 12 2.160 2.282 2.650 3.012 3.372 3.852 4.221 0.692 0.868 1.076 2.145 2.264 2.624 2.977 3.326 3.787 4.140 14 0.691 0.866 1.074 1.753 2.131 2.249 2.602 2.947 3.286 3.733 4.073 15 0.690 0.865 1.337 2.120 2.235 2.583 2.921 3.252 3.686 4.015 16 2.898 3.222 3.646 3.965 2101 2:592 3.197 3.610 3.922 18 0.861 2.093 2530 2.861 3.174 3.883 0.687 0.860 .325 2.086 2.197 2.845 3.153 3.850 20 2.080 2.518 2.074 2508 2.831 2.819 3.792 2.069 2.17 2.500 3.768 .318 2.172 3.09 3.745 0.856 1.058 .316 1.708 2.060 2.16 2.485 2.787 3.450 3.725 0.684 0.856 1.058 .315 1.706 2.056 2.479 2.779 3.435 3.707 1.057 1.703 2.052 2.162 2.473 2.771 3.421 WE 2.048 2.154 2.467 3.047 3.674 0.683 310 2.045 1.697 2.042 2.147 2.457 2.756 2.750 3.030 3. 646 0.682 0.853 1.309 1.696 2.040 2.144 2.453 2.744 3.022 3.375 3.633 1.309 .694 2.037 2.141 2.738 3.015 3.622 0.853 1.308 2.035 2.138 2:728 3.008 3.611 0.852 307 2032 2.136 34 0.682 0.852 1.052 1.306 .690 2.030 2.133 2.438 2:724 2.996 .340 3.591 2.028 2.131 2.434 2.719 3.333 3.582 36 2.026 2.129 2431 2.715 3.326 3.574 37 2.024 2.980 1.050 2.125 2 426 2.712 3.319 2.976 3.558 39 0.681 0.851 1.050 2.021 2.123 2.423 2.704 2.971 3.307 3.551 0.679 0.849 1.047 1.676 2.009 2.109 2403 2.678 2.937 3.261 50 0.679 0.848 1.045 1.671 2.000 2.099 2.660 2.915 3.232 3.460 0.678 3.435 50 0.678 0.846 1.043 2 088 2.374 2.639 2. 887 3.195 3.416 0.677 0.846 1.042 2.084 2.368 2.632 2.878 3.183 3.402 90 0.677 0.845 1.042 1.660 2.081 2.626 2.871 3.174 3.390 190 1060 1.037 2.056 2:330 2 581 3.098 3.300 1000 0.674 1.036 2.054 2.576 3.291 df 0.25 0.20 0.15 0.10 0.05 0.025 0.02 0.01 0.005 0.0025 0.001 0.0005 df Print Done Clear All Check Answer Textbook StatCrunch Get More Help -7 To test Ho: H = 107 versus H1: H # 107 a simple random sample of size n = 35 is obtained. Complete parts a through e below. - X Click here to view the t-Distribution Area in Right Tail. t-Distribution Area in Right Tail (a) Does the population have to be normally distributed to test this hypothesis? Why? O A. No, because the test is two-tailed. t-Distribution Area in Right Tail O B. Yes, because the sample is random. df 0.25 0.20 0.15 0.10 0.05 0.025 0.02 0.01 0.005 0.0025 0.001 .0005 df C. No, because n 2 30. 636.619 D. Yes, because n 2 30. 2 1.000 1-370 1.963 3.078 6.314 12.706 5.894 1.821 63.657 7.321 9.925 1.089 18.309 0.816 1.061 0.978 1.386 1.638 2.920 4.303 6.965 22.327 31.599 0.765 10.215 12.924 (b) If x = 104.0 and s = 5.8, compute the test statistic. 0.741 0.941 1.250 1.190 1.533 2.353 3.182 2.132 2.776 2.999 3 747 4.60 5.598 7.173 8.610 5 0.727 0.920 1.156 1.476 2571 2.757 3.365 4.032 4.773 5.893 6.869 The test statistic is to = . (Round to two decimal places as needed.) 6 0.718 0.906 1.134 1.440 1.943 2.447 2.612 3.143 3.707 4.317 5.208 5.959 1.415 2.365 2.517 2.998 3.499 4.785 5 408 7 0.711 0.896 1.119 8 0.706 0.889 1.108 1.860 2.306 3.833 4:501 5.041 0.703 0.883 1.100 1.383 1.833 2.262 2.398 2.821 3.250 3.690 4.297 4.781 10 0.700 0.879 1.093 1.372 1.812 2.228 2.359 2.764 3.169 3.581 4.144 4.587 10 11 0.697 0.876 1.088 2.201 2.328 2.718 3.106 3.497 4.025 4.437 11 12 0.695 0.873 3:179 2.303 2.681 3.059 3:372 3.930 4.318 12 2.282 3.012 3.852 14 0.692 0.868 2 977 3.787 14 15 0.691 0.866 1.074 2.131 3.32 2. 249 2.602 2.94 3.286 3,733 4.073 15 16 0.690 0.865 1.071 1.746 2.120 2.235 2.583 2.92 3.686 4.015 3.965 18 2.101 2.214 2.552 3.610 2.093 2539 3.579 3.88 0.687 0.860 2.086 2.197 2.528 2.845 3.153 3.552 3.850 0.686 0.859 1.063 1.721 2.080 2.189 2.518 3.527 3.819 3.505 3.792 0.858 1.714 2.069 2 500 3.768 0.685 0.857 1.059 1318 2.492 2.797 3.467 3:745 0.684 0.856 1.058 1 316 1.708 2.060 2.167 2 485 2.787 3.450 3.725 0.684 1.058 1.315 2.056 2.162 2479 3.067 3.435 3.707 0.684 0.855 .314 2.052 2.473 3.421 3.690 0.855 2.048 2.467 3.408 3.674 0.683 0.854 1.311 2.045 3.659 0.683 0.854 1.310 2.042 2. 147 2.457 2.750 3.030 3.385 3.646 0.682 0.853 1.309 2.040 2.144 2.453 2.744 :022 3.375 3.633 0 . 682 2.037 2:449 2.738 3.015 3.622 2 445 0.852 35 0.682 1.307 2.733 0.682 0.852 1.052 1.306 2.030 2.133 3.60 2.438 2.724 2.996 3.591 0.681 0.852 1.052 1.306 1.688 2.028 2.131 2.434 2.719 2.990 3.333 3.582 36 0.851 1.051 1.305 1.687 2.026 2.129 2.431 2.715 2.985 3.574 37 0.851 1 304 3.319 0.851 1.050 2.023 2.426 2.976 3.56 3.558 39 40 0.681 0.851 1.050 1.303 1.684 2.021 2.123 2.423 2: 704 2.971 3.307 0.679 1.676 2.009 2.109 2.403 2.678 2.937 3.261 50 0.679 1.045 2.000 2.099 2.660 2.915 3.232 0.678 1.044 2.093 2.899 0.678 1.043 1.292 2.088 2.639 2.887 3.195 3.416 0.677 0.846 1.042 1291 1.662 1.987 2.084 2.368 2.632 2.878 3.183 3.402 90 100 0.845 1.042 1.290 1.660 2.081 2.364 2.626 2.871 3.174 190 0.677 1060 1.037 1.282 1.646 2.056 2.330 2.581 2.813 3.098 3.300 1090 0.675 0.842 0.674 0.842 1.036 1782 1.645 2.326 2.576 3.291 z df 0.25 0.20 0.15 0.10 0.05 0.025 0.02 0.01 0.005 0.0025 0.001 .0005 df Print Done Clear All Check Answer Help Me Solve This View an Example Get More Help -A college entrance exam company determined that a score of 21 on the mathematics portion of the exam suggests that a student is ready for college-level mathematics. To achieve this goal, the company recommends that students take a core curriculum of math courses in high school. Suppose a random sample of 250 students who completed this core set of courses results in a mean math score of 21.4 on the college entrance exam with a standard deviation of 3.9. Do these results suggest that students who complete the core curriculum are ready for college-level mathematics? That is, are they scoring above 21 on the mathematics portion of the exam? Complete parts a) through d) below. Click the icon to view the table of critical t-values. (a) State the appropriate null and alternative hypotheses. Fill in the correct answers below. X The appropriate null and alternative hypotheses are Ho: H = 21 versus H1: H > 21 . Table of Critical t-Values (Type integers or decimals. Do not round.) (b) Verify that the requirements to perform the test using the t-distribution are satisfied. Select all that apply. LY A. The students' test scores were independent of one another. right ta LY B. The sample size is larger than 30. C. The sample data come from a population that is approximately normal. 1-Distribution LY D. The students were randomly sampled. Area in Right Tail E. A boxplot of the sample data shows no outliers. df 0.25 0.20 0.15 0.10 0.05 0.025 0.02 0.01 0.005 0.0025 0.001 0.0005 df F. None of the requirements are satisfied. 3.078 1314 2.706 8.309 36.619 3.182 3.482 12.92 (c) Use the P-value approach at the a = 0.10 level of significance to test the hypotheses in part (a). 2.909 8.610 1.476 2.757 6.869 Identify the test statistic. 1.440 1.943 2365 2.612 5.208 5.959 4.785 5.408 to =(Round to two decimal places as needed.) 4:587 4.437 3.733 4.073 3.686 4.015 2.990 3.333 3.551 3.232 3.435 3.402 3.390 192939 3 300 0.25 0.20 0.15 0.10 0.025 0.02 0.01 0.005 0.0025 0.001 0.0005 df Clear All Check Answer Help Me Solve This View an Example Get More Help