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Tesearcher in the team, has randomly selected a sample of 25 male runners from a high school and the time (in seconds) for each of them to complete a 400-meter race was recorded. The sample mean running time was 53 seconds. It is assumed that the running time in a 400-meter race follows a normal distribution with a population standard deviation of 5.5 seconds. (a) Give a point estimate of the population mean running time for a 400-meter race. (b) Calculate the sampling error at 95% confidence level. (c) Construct a 95% confidence interval estimate of the population mean running time for a 400-meter race. (d) If instead of 25, 80 male runners are selected for the study, what is the sampling error at 95% confidence level? When the 95% confidence interval is constructed based on a sample with 80 male runners, would you expect the interval will be (I) narrower, (II) wider, or (III) the same width as the confidence interval constructed in part (c)? (e) After discussion with the research director, Jimmy is asked to work on the research again. This time, he needs to ensure the difference between the point estimate and the true population mean be within +0.8 seconds at 99% confidence level. To fulfil the requirement, how large should be the minimum sample size?

Tesearcher in the team, has randomly selected a sample of 25 male runners from a high school and the time (in seconds) for each of them to complete a 400-meter race was recorded. The sample mean running time was 53 seconds. It is assumed that the running time in a 400-meter race follows a normal distribution with a population standard deviation of 5.5 seconds. (a) Give a point estimate of the population mean running time for a 400-meter race. (b) Calculate the sampling error at 95% confidence level. (c) Construct a 95% confidence interval estimate of the population mean running time for a 400-meter race. (d) If instead of 25, 80 male runners are selected for the study, what is the sampling error at 95% confidence level? When the 95% confidence interval is constructed based on a sample with 80 male runners, would you expect the interval will be (I) narrower, (II) wider, or (III) the same width as the confidence interval constructed in part (c)? (e) After discussion with the research director, Jimmy is asked to work on the research again. This time, he needs to ensure the difference between the point estimate and the true population mean be within +0.8 seconds at 99% confidence level. To fulfil the requirement, how large should be the minimum sample size?

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section: Chapter Questions
Problem 7MCQ
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三转文档 日单页 D双页、工连续阅读 背景,划词翻译 截屏。压缩全屏显示 播放 A research team is working on a project to study the time (in seconds) for high school male runners to finish a 400-meter race. Jimmy, a junior researcher in the team, has randomly selected a sample of 25 male runners from a high school and the time (in seconds) for each of them to complete a 400-meter race was recorded. The sample mean running time was 53 seconds. It is assumed that the running time in a 400-meter race follows a normal distribution with a population standard deviation of 5.5 seconds. (a) Give a point estimate of the population mean running time for a 400-meter race. (b) Calculate the sampling error at 95% confidence level. (c) Construct a 95% confidence interval estimate of the population mean running time for a 400-meter race. (d) If instead of 25, 80 male runners are selected for the study, what is the sampling error at 95% confidence level? When the 95% confidence interval is constructed based on a sample with 80 male runners, would you expect the interval will be (I) narrower, (II) wider, or (III) the same width as the confidence interval constructed in part (c)? (e) After discussion with the research director, Jimmy is asked to work on the research again. This time, he needs to ensure the difference between the point estimate and the true population mean be within ±0.8 seconds at 99% confidence level. To fulfil the requirement, how large should be the minimum sample size? 102 %
Transcribed Image Text:三转文档 日单页 D双页、工连续阅读 背景,划词翻译 截屏。压缩全屏显示 播放 A research team is working on a project to study the time (in seconds) for high school male runners to finish a 400-meter race. Jimmy, a junior researcher in the team, has randomly selected a sample of 25 male runners from a high school and the time (in seconds) for each of them to complete a 400-meter race was recorded. The sample mean running time was 53 seconds. It is assumed that the running time in a 400-meter race follows a normal distribution with a population standard deviation of 5.5 seconds. (a) Give a point estimate of the population mean running time for a 400-meter race. (b) Calculate the sampling error at 95% confidence level. (c) Construct a 95% confidence interval estimate of the population mean running time for a 400-meter race. (d) If instead of 25, 80 male runners are selected for the study, what is the sampling error at 95% confidence level? When the 95% confidence interval is constructed based on a sample with 80 male runners, would you expect the interval will be (I) narrower, (II) wider, or (III) the same width as the confidence interval constructed in part (c)? (e) After discussion with the research director, Jimmy is asked to work on the research again. This time, he needs to ensure the difference between the point estimate and the true population mean be within ±0.8 seconds at 99% confidence level. To fulfil the requirement, how large should be the minimum sample size? 102 %
The entries in Table I are the probabilities that a random variable having the standard normal distribution will take on a value between 0 andz. They are given by the area of the gray region under the curve in the figure, The entries in Table II are values for which the area to their right under the distribution with given degrees of freedom (the gray area in the figure) is equal to a . TABLE II VALUE OFt TABLE I NORMAL-CURVE AREAS d.f. fo.025 lo010 fo 005 JP 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 1 6.314 12.706 31.821 63.657 0.0 0.0000 0.0040 0.0080 0.0120 0.0160 0.0199 0.0239 0.0279 0.0319 0.0359 2 2.920 4.303 6.965 9.925 2 0.1 0.0398 0.0438 0.0478 0.0517 0.0557 0.0596 0.0636 0.0675 0.0714 0.0753 2.353 3.182 4.541 5.841 3 0.2 0.0793 0.0832 0.0871 0.0910 0.0987 0.0948 0.1331 0.1026 0.1064 0.1103 0.1141 4 2.132 2.776 3.747 4.604 4. 0.1406 0.1772 0.3 0.1179 0.1217 0.1255 0.1293 0.1368 0.1443 0.1480 0.1517 5 2.015 2.571 3.365 4.032 0.1554 0.1915 0.4 0.1591 0.1628 0.1664 0.1700 0.1736 0.1808 0.1844 0.1879 0.5 0.1950 0.1985 0.2019 0.2054 0.2088 0.2123 0.2157 0.2190 0.2224 6. 1.943 2.447 3.143 3.707 6. 7. 0.2291 0.2611 0.6 0.2257 0.2324 0.2357 0.2389 0.2422 0.2454 0.2486 0.2517 0.2549 7 1.895 2.365 2.998 3.499 0.7 0.2580 0.2642 0.2673 0.2704 0.2734 0.2764 0.2794 0.2823 0.2852 0.3133 8. 1.860 2.306 2.896 3.355 8. 0.8 0.2881 0.2910 0.2939 0.2967 0.2995 0.3023 0.3051 0.3078 0.3106 9. 1.833 2.262 2.821 3.250 9. 0.3365 0.3389 0.3599 0.3621 0.9 0.3159 0.3186 0.3212 0.3238 0.3264 0.3289 0.3315 0.3340 10 1.812 2.228 2.764 3.169 10 1.0 0.3413 0.3438 0.3461 0.3485 0.3508 0.3531 0.3554 0.3577 1.1 0.3643 0.3665 0.3686 11 1.796 2.201 2.718 3.106 11 0.3708 0.3907 0.3729 0.3749 0.3770 0.3790 0.3810 0.3830 0.3849 0.4032 1.2 0.3869 0.3888 0.3925 0.3944 0.3962 0.4131 0.3980 0.4147 0.3997 0.4015 0.4162 0.4177 12 1.782 2.179 2.681 3.055 12 1.3 0.4049 0.4066 0.4082 0.4099 0.4115 13 1.771 2.160 2.650 3.012 13 1.4 0.4192 0.4207 0,4222 0.4236 0.4251 0.4265 0.4279 0.4292 0.4306 0.4319 14 1.761 2.145 2,624 2.977 14 1.5 0.4332 0.4345 0.4357 0.4370 0.4382 0.4394 0.4406 0.4418 0.4429 0.4441 15 1.753 2.131 2.602 2.947 15 0.4505 0.4599 1.6 0.4452 0.4463 0.4474 0.4484 0.4495 0.4515 0.4525 0.4535 0.4545 0.4582 0.4591 0.4608 0.4616 2.120 0.4625 0.4699 0.4706 0.4767 1.7 0.4554 0.4564 0.4573 0.4633 16 1.746 2.583 2.921 16 1.8 0.4641 0.4648 0.4656 0.4664 0.4671 0.4678 0.4685 0.4692 17 1.740 2.110 2.567 2.898 17 0.4725 0.4783 0.4732 0.4788 0,4738 0,4793 1.9 0.4713 0.4719 0.4744 0.4750 0.4756 0.4761 18 1.734 2.101 2.552 2.878 18 2.0 0.4772 0.4778 0.4798 0.4803 0.4808 0.4812 0.4817 19 1.729 2.093 2,539 2.861 19 0.4834 0.4871 0.4850 0.4884 0.4854 0.4857 0.4887 0.4890 0.4826 0.4830 0.4838 0.4875 2.1 0.4821 0.4842 0.4846 20 1.725 2.086 2.528 2.845 20 0.4864 0.4896 2.2 0.4861 0.4868 0.4878 0.4881 0.4898 0.4922 0.4909 0.4931 0.4916 0.4893 0.4918 2.3 0.4901 0.4904 0.4906 0.4911 0.4913 21 1.721 2,080 2.518 2.831 21 2.4 0.4920 0.4925 0.4927 0.4929 0.4932 0.4934 0.4936 22 1.717 2.074 2.508 2.819 22 2.5 0.4938 0.4940 0.4941 0.4943 0.4945 0.4946 0.4948 0.4949 0.4951 0.4952 23 1.714 2.069 2.500 2.807 23 0.4956 0.4967 0.4960 0.4970 0.4962 0.4972 0.4959 0.4964 0.4955 0.4966 2.6 0.4953 0.4957 0.4961 0.4963 24 1.711 2.064 2.492 2.797 24 0.4971 0.4973 0.4980 2.7 0.4965 0.4968 0.4969 0.4974 25 1.708 2.060 2.485 2.787 25 2.8 0.4974 0.4975 0.4976 0.4977 0.4977 0.4978 0.4979 0.4979 0.4981 0.4986 0.4990 0.4984 0.4985 0.4986 0.4990 2.9 0.4981 0.4982 0.4982 0.4983 0.4984 0.4985 26 1.706 2.056 2.479 2.779 26 3.0 0.4987 0.4987 0.4987 0.4988 0.4988 0.4989 0.4989 0.4989 27 1.703 2.052 2.473 2.771 27 Also, for z= 4.0, 5.0 and 6.0, the areas are 0.49997, 0.4999997, and 0.499999999. 28 1.701 2.048 2,467 2.763 28 29 1.699 2.045 2.462 2.756 29 Inf. 1.645 1.960 2.326 2.576 Inf. 0本地备份开
Transcribed Image Text:The entries in Table I are the probabilities that a random variable having the standard normal distribution will take on a value between 0 andz. They are given by the area of the gray region under the curve in the figure, The entries in Table II are values for which the area to their right under the distribution with given degrees of freedom (the gray area in the figure) is equal to a . TABLE II VALUE OFt TABLE I NORMAL-CURVE AREAS d.f. fo.025 lo010 fo 005 JP 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 1 6.314 12.706 31.821 63.657 0.0 0.0000 0.0040 0.0080 0.0120 0.0160 0.0199 0.0239 0.0279 0.0319 0.0359 2 2.920 4.303 6.965 9.925 2 0.1 0.0398 0.0438 0.0478 0.0517 0.0557 0.0596 0.0636 0.0675 0.0714 0.0753 2.353 3.182 4.541 5.841 3 0.2 0.0793 0.0832 0.0871 0.0910 0.0987 0.0948 0.1331 0.1026 0.1064 0.1103 0.1141 4 2.132 2.776 3.747 4.604 4. 0.1406 0.1772 0.3 0.1179 0.1217 0.1255 0.1293 0.1368 0.1443 0.1480 0.1517 5 2.015 2.571 3.365 4.032 0.1554 0.1915 0.4 0.1591 0.1628 0.1664 0.1700 0.1736 0.1808 0.1844 0.1879 0.5 0.1950 0.1985 0.2019 0.2054 0.2088 0.2123 0.2157 0.2190 0.2224 6. 1.943 2.447 3.143 3.707 6. 7. 0.2291 0.2611 0.6 0.2257 0.2324 0.2357 0.2389 0.2422 0.2454 0.2486 0.2517 0.2549 7 1.895 2.365 2.998 3.499 0.7 0.2580 0.2642 0.2673 0.2704 0.2734 0.2764 0.2794 0.2823 0.2852 0.3133 8. 1.860 2.306 2.896 3.355 8. 0.8 0.2881 0.2910 0.2939 0.2967 0.2995 0.3023 0.3051 0.3078 0.3106 9. 1.833 2.262 2.821 3.250 9. 0.3365 0.3389 0.3599 0.3621 0.9 0.3159 0.3186 0.3212 0.3238 0.3264 0.3289 0.3315 0.3340 10 1.812 2.228 2.764 3.169 10 1.0 0.3413 0.3438 0.3461 0.3485 0.3508 0.3531 0.3554 0.3577 1.1 0.3643 0.3665 0.3686 11 1.796 2.201 2.718 3.106 11 0.3708 0.3907 0.3729 0.3749 0.3770 0.3790 0.3810 0.3830 0.3849 0.4032 1.2 0.3869 0.3888 0.3925 0.3944 0.3962 0.4131 0.3980 0.4147 0.3997 0.4015 0.4162 0.4177 12 1.782 2.179 2.681 3.055 12 1.3 0.4049 0.4066 0.4082 0.4099 0.4115 13 1.771 2.160 2.650 3.012 13 1.4 0.4192 0.4207 0,4222 0.4236 0.4251 0.4265 0.4279 0.4292 0.4306 0.4319 14 1.761 2.145 2,624 2.977 14 1.5 0.4332 0.4345 0.4357 0.4370 0.4382 0.4394 0.4406 0.4418 0.4429 0.4441 15 1.753 2.131 2.602 2.947 15 0.4505 0.4599 1.6 0.4452 0.4463 0.4474 0.4484 0.4495 0.4515 0.4525 0.4535 0.4545 0.4582 0.4591 0.4608 0.4616 2.120 0.4625 0.4699 0.4706 0.4767 1.7 0.4554 0.4564 0.4573 0.4633 16 1.746 2.583 2.921 16 1.8 0.4641 0.4648 0.4656 0.4664 0.4671 0.4678 0.4685 0.4692 17 1.740 2.110 2.567 2.898 17 0.4725 0.4783 0.4732 0.4788 0,4738 0,4793 1.9 0.4713 0.4719 0.4744 0.4750 0.4756 0.4761 18 1.734 2.101 2.552 2.878 18 2.0 0.4772 0.4778 0.4798 0.4803 0.4808 0.4812 0.4817 19 1.729 2.093 2,539 2.861 19 0.4834 0.4871 0.4850 0.4884 0.4854 0.4857 0.4887 0.4890 0.4826 0.4830 0.4838 0.4875 2.1 0.4821 0.4842 0.4846 20 1.725 2.086 2.528 2.845 20 0.4864 0.4896 2.2 0.4861 0.4868 0.4878 0.4881 0.4898 0.4922 0.4909 0.4931 0.4916 0.4893 0.4918 2.3 0.4901 0.4904 0.4906 0.4911 0.4913 21 1.721 2,080 2.518 2.831 21 2.4 0.4920 0.4925 0.4927 0.4929 0.4932 0.4934 0.4936 22 1.717 2.074 2.508 2.819 22 2.5 0.4938 0.4940 0.4941 0.4943 0.4945 0.4946 0.4948 0.4949 0.4951 0.4952 23 1.714 2.069 2.500 2.807 23 0.4956 0.4967 0.4960 0.4970 0.4962 0.4972 0.4959 0.4964 0.4955 0.4966 2.6 0.4953 0.4957 0.4961 0.4963 24 1.711 2.064 2.492 2.797 24 0.4971 0.4973 0.4980 2.7 0.4965 0.4968 0.4969 0.4974 25 1.708 2.060 2.485 2.787 25 2.8 0.4974 0.4975 0.4976 0.4977 0.4977 0.4978 0.4979 0.4979 0.4981 0.4986 0.4990 0.4984 0.4985 0.4986 0.4990 2.9 0.4981 0.4982 0.4982 0.4983 0.4984 0.4985 26 1.706 2.056 2.479 2.779 26 3.0 0.4987 0.4987 0.4987 0.4988 0.4988 0.4989 0.4989 0.4989 27 1.703 2.052 2.473 2.771 27 Also, for z= 4.0, 5.0 and 6.0, the areas are 0.49997, 0.4999997, and 0.499999999. 28 1.701 2.048 2,467 2.763 28 29 1.699 2.045 2.462 2.756 29 Inf. 1.645 1.960 2.326 2.576 Inf. 0本地备份开
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