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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.

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.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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.

The entries in Table I are the probabilities that a random variable having the standard normal distribution will take on a value between 0 and:. They are given by the area of the gray region under the curve in the figure. TABLE I NORMAL-CURVE AREAS 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.0000 0.0040 0.0080 0.0120 0.0160 0.0199 0.0239 0.0279 0.0319 0.0359 0.0398 0.0793 0.0438 0.0832 0.0675 0.1064 0.0517 0.0636 0.1026 0.1 0.0478 0.0557 0.0596 0.0714 0.0753 0.2 0.0871 0.0910 0.0948 0.0987 0.1103 0.1141 0.3 0.1179 0.1217 0.1255 0.1293 0.1331 0.1368 0.1406 0.1443 0.1480 0.1517 0.4 0.1554 0.1591 0.1628 0.1664 0.1700 0.1736 0.1772 0.1808 0.1844 0.1879 0.5 0.1915 0.1950 0.1985 0.2019 0.2054 0.2088 0.2123 0.2157 0.2190 0.2224 0.2257 0.2580 0.2324 0.2642 0.2357 0.2673 0.2389 0.2704 0.2422 0.2734 0.2517 0.2823 0.2549 0.2852 0.6 0.2291 0.2454 0.2486 0.7 0.2611 0.2764 0.2794 0.8 0.3159 0.3413 0.2881 0.2910 0.2939 0.2967 0.2995 0.3023 0.3051 0.3078 0.3106 0.3133 0.9 0.3186 0.3212 0.3238 0.3264 0.3289 0.3315 0.3340 0.3365 0.3389 1.0 0.3438 0.3461 0.3485 0.3508 0.3531 0.3554 0.3577 0.3599 0.3621 0.3686 0.3888 0.4066 0.3770 0.3962 0.4131 1.1 0.3643 0.3665 0.3708 0.3729 0.3749 0.3790 0.3810 0.3830 0.3849 0.4032 0.3907 0.4082 0.4236 0.3997 0.4162 0.4306 0.3869 0.3925 0.4099 0.4251 1.2 0.3944 0.3980 0.4015 0.4049 0.4207 1.3 0.4115 0.4147 0.4177 1.4 0.4192 0.4222 0.4265 0.4279 0.4292 0.4319 1.5 0.4332 0.4345 0.4357 0.4370 0.4382 0.4394 0.4406 0.4418 0.4429 0.4441 0.4484 0.4582 0.4664 0.4535 0.4625 0.4699 1.6 0.4452 0.4463 0.4474 0.4495 0.4505 0.4515 0.4525 0.4545 0.4554 0.4641 0.4564 0.4648 0.4591 0.4671 0.4608 0.4685 0.4616 0.4692 0.4633 0.4706 1.7 0.4573 0.4599 1.8 0.4656 0.4678 1.9 0.4713 0.4719 0.4725 0.4732 0.4738 0.4744 0.4750 0.4756 0.4761 0.4767 2.0 0.4772 0.4778 0.4783 0.4788 0.4793 0.4798 0.4803 0.4808 0.4812 0.4817 0.4821 0.4861 0.4834 0.4871 0.4901 0.4838 0.4875 0.4904 0.4846 0.4881 0.4909 0.4857 0.4890 2.1 0.4826 0.4830 0.4842 0.4850 0.4854 0.4875 0.4906 0.4887 0.4913 2.2 0.4864 0.4868 0.4884 2.3 0.4893 0.4896 0.4898 0.4911 0.4916 2.4 0.4918 0.4920 0.4922 0.4925 0.4927 0.4929 0.4931 0.4932 0.4934 0.4936 2.5 0.4938 0.4940 0.4941 0.4943 0.4945 0.4946 0.4948 0.4949 0.4951 0.4952 0.4957 0.4968 0.4963 0.4973 0.4953 0.4955 0.4966 0.4959 0.4969 2.6 0.4956 0.4960 0.4961 0.4962 0.4964 0.4974 2.7 0.4965 0.4967 0.4970 0.4971 0.4972 2.8 0.4974 0.4975 0.4976 0.4977 0.4977 0.4978 0.4979 0.4979 0.4980 0.4981 2.9 0.4981 0.4982 0.4982 0.4983 0.4984 0.4984 0.4985 0.4985 0.4986 0.4986 3.0 0.4987 0.4987 0.4987 0.4988 0.4988 0.4989 0.4989 0.4989 0.4990 0.4990 Also, for z= 4.0, 5.0 and 6.0, the areas are 0.49997, 0.4999997, and 0.499999999.
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 and:. They are given by the area of the gray region under the curve in the figure. TABLE I NORMAL-CURVE AREAS 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.0000 0.0040 0.0080 0.0120 0.0160 0.0199 0.0239 0.0279 0.0319 0.0359 0.0398 0.0793 0.0438 0.0832 0.0675 0.1064 0.0517 0.0636 0.1026 0.1 0.0478 0.0557 0.0596 0.0714 0.0753 0.2 0.0871 0.0910 0.0948 0.0987 0.1103 0.1141 0.3 0.1179 0.1217 0.1255 0.1293 0.1331 0.1368 0.1406 0.1443 0.1480 0.1517 0.4 0.1554 0.1591 0.1628 0.1664 0.1700 0.1736 0.1772 0.1808 0.1844 0.1879 0.5 0.1915 0.1950 0.1985 0.2019 0.2054 0.2088 0.2123 0.2157 0.2190 0.2224 0.2257 0.2580 0.2324 0.2642 0.2357 0.2673 0.2389 0.2704 0.2422 0.2734 0.2517 0.2823 0.2549 0.2852 0.6 0.2291 0.2454 0.2486 0.7 0.2611 0.2764 0.2794 0.8 0.3159 0.3413 0.2881 0.2910 0.2939 0.2967 0.2995 0.3023 0.3051 0.3078 0.3106 0.3133 0.9 0.3186 0.3212 0.3238 0.3264 0.3289 0.3315 0.3340 0.3365 0.3389 1.0 0.3438 0.3461 0.3485 0.3508 0.3531 0.3554 0.3577 0.3599 0.3621 0.3686 0.3888 0.4066 0.3770 0.3962 0.4131 1.1 0.3643 0.3665 0.3708 0.3729 0.3749 0.3790 0.3810 0.3830 0.3849 0.4032 0.3907 0.4082 0.4236 0.3997 0.4162 0.4306 0.3869 0.3925 0.4099 0.4251 1.2 0.3944 0.3980 0.4015 0.4049 0.4207 1.3 0.4115 0.4147 0.4177 1.4 0.4192 0.4222 0.4265 0.4279 0.4292 0.4319 1.5 0.4332 0.4345 0.4357 0.4370 0.4382 0.4394 0.4406 0.4418 0.4429 0.4441 0.4484 0.4582 0.4664 0.4535 0.4625 0.4699 1.6 0.4452 0.4463 0.4474 0.4495 0.4505 0.4515 0.4525 0.4545 0.4554 0.4641 0.4564 0.4648 0.4591 0.4671 0.4608 0.4685 0.4616 0.4692 0.4633 0.4706 1.7 0.4573 0.4599 1.8 0.4656 0.4678 1.9 0.4713 0.4719 0.4725 0.4732 0.4738 0.4744 0.4750 0.4756 0.4761 0.4767 2.0 0.4772 0.4778 0.4783 0.4788 0.4793 0.4798 0.4803 0.4808 0.4812 0.4817 0.4821 0.4861 0.4834 0.4871 0.4901 0.4838 0.4875 0.4904 0.4846 0.4881 0.4909 0.4857 0.4890 2.1 0.4826 0.4830 0.4842 0.4850 0.4854 0.4875 0.4906 0.4887 0.4913 2.2 0.4864 0.4868 0.4884 2.3 0.4893 0.4896 0.4898 0.4911 0.4916 2.4 0.4918 0.4920 0.4922 0.4925 0.4927 0.4929 0.4931 0.4932 0.4934 0.4936 2.5 0.4938 0.4940 0.4941 0.4943 0.4945 0.4946 0.4948 0.4949 0.4951 0.4952 0.4957 0.4968 0.4963 0.4973 0.4953 0.4955 0.4966 0.4959 0.4969 2.6 0.4956 0.4960 0.4961 0.4962 0.4964 0.4974 2.7 0.4965 0.4967 0.4970 0.4971 0.4972 2.8 0.4974 0.4975 0.4976 0.4977 0.4977 0.4978 0.4979 0.4979 0.4980 0.4981 2.9 0.4981 0.4982 0.4982 0.4983 0.4984 0.4984 0.4985 0.4985 0.4986 0.4986 3.0 0.4987 0.4987 0.4987 0.4988 0.4988 0.4989 0.4989 0.4989 0.4990 0.4990 Also, for z= 4.0, 5.0 and 6.0, the areas are 0.49997, 0.4999997, and 0.499999999.
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 figuure) is equal to a . t TABLE II VALUE OFt d.f. f0.050 f0.025 fo.010 f0.005 d.f 1 6.314 12.706 31.821 63.657 1 2.920 4.303 6.965 9.925 2.353 3.182 4.541 5.841 4 2.132 2.776 3.747 4.604 4 5 2.015 2.571 3.365 4.032 1.943 2.447 3.143 3.707 6 7 1.895 2.365 2.998 3.499 7 1.860 2.306 2.896 3.355 9 1.833 2.262 2.821 3.250 9 10 1.812 2.228 2.764 3.169 10 11 1.796 2.201 2.718 3.106 11 12 1.782 2.179 2.681 3.055 12 13 1.771 2.160 2.650 3.012 13 14 1.761 2.145 2.624 2.977 14 15 1.753 2.131 2.602 2.947 15 16 1.746 2.120 2.583 2.921 16 17 1.740 2.110 2.567 2.898 17 18 1.734 2.101 2.552 2.878 18 19 1.729 2.093 2.539 2.861 19 20 1.725 2.086 2.528 2.845 20 21 1.721 2.080 2.518 2.831 21 22 1.717 2.074 2.508 2.819 22 23 1.714 2.069 2.500 2.807 23 24 1.711 2.064 2.492 2.797 24 25 1.708 2.060 2485 2.787 25 26 1.706 2.056 2.479 2.779 26 27 1.703 2.052 2.473 2.771 27 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 In.
Transcribed Image Text: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 figuure) is equal to a . t TABLE II VALUE OFt d.f. f0.050 f0.025 fo.010 f0.005 d.f 1 6.314 12.706 31.821 63.657 1 2.920 4.303 6.965 9.925 2.353 3.182 4.541 5.841 4 2.132 2.776 3.747 4.604 4 5 2.015 2.571 3.365 4.032 1.943 2.447 3.143 3.707 6 7 1.895 2.365 2.998 3.499 7 1.860 2.306 2.896 3.355 9 1.833 2.262 2.821 3.250 9 10 1.812 2.228 2.764 3.169 10 11 1.796 2.201 2.718 3.106 11 12 1.782 2.179 2.681 3.055 12 13 1.771 2.160 2.650 3.012 13 14 1.761 2.145 2.624 2.977 14 15 1.753 2.131 2.602 2.947 15 16 1.746 2.120 2.583 2.921 16 17 1.740 2.110 2.567 2.898 17 18 1.734 2.101 2.552 2.878 18 19 1.729 2.093 2.539 2.861 19 20 1.725 2.086 2.528 2.845 20 21 1.721 2.080 2.518 2.831 21 22 1.717 2.074 2.508 2.819 22 23 1.714 2.069 2.500 2.807 23 24 1.711 2.064 2.492 2.797 24 25 1.708 2.060 2485 2.787 25 26 1.706 2.056 2.479 2.779 26 27 1.703 2.052 2.473 2.771 27 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 In.
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