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The random sample shown below was selected from a normal distribution. 8,3,7,3,9,6 & Complete parts a and b. a. Construct a 99% confidence interval for the population mean p. (| , ) (Round to two decimal places as needed.) b. Assume that sample mean x and sample standard deviation s remain exactly the same as those you just calculated but that are based on a sample of n = 25 observations. Repeat part a. What is the effect of increasing the sample size on the width of the confidence intervals? The confidence interval is ( , ) . (Round to two decimal places as needed.) What is the effect of the sample size on the width of the confidence interval? () A. As the sample size increases, the width increases. (1) B. As the sample size increases, the width stays the same. () . As the sample size increases, the width decreases. In a psychology journal, researchers reported that a chief executive officer's facial structure can be used to predict a firm's financial performance. The study involved measuring the facial width-to-height ratio (WHR) for each in a sample of 51 CEOs at publicly traded Fortune 500 firms. These WHR values (determined by computer analyzing a photo of the CEQ's face) had a mean ofx=1.91and a standard deviation of s =0.11. Use this information to complete parts a and b below. a. Find and interpret a 95% confidence interval for p, the mean facial WHR for all CEOs at publicly ~ # traded Fortune 500 firms. (Round to three decimal places as needed.) () A. The 95% confidence interval for mean facial WHR score indicates that 95% of CEOs in the sample have a WHR between and (_) B. The 95% confidence interval for mean facial WHR indicates that the true mean facial WHR for the CEOs in the sample is between and with 95% confidence. (_) . The 95% confidence interval for mean facial WHR indicates that 95% of all CEOs at publicly traded Fortune 500 firms have a WHR between and . v () D. The 95% confidence interval for mean facial WHR indicates that the true mean facial WHR for all CEOs at publicly traded Fortune 500 firms is between and with 95% confidence. b. The researchers found that CEOs with wider faces (relative to height) tended to be associated with firms that had greater financial performance. They based their inference on an equation that uses facial WHR to predict financial performance. Suppose an analyst wants to predict the financial performance of a Fortune 500 firm based on the value of the true mean facial WHR of CEOs. The analyst wants to use the value of p=2.1. Do you recommend the use this value? . Yes, since the suggested value of p lies within the confidence interval from part a, it is reasonable to assume that it is the true mean facial WHR of CEOs. No, since the suggested value of p would be a usual value to obtain in a sample of 51 CEOs, itis not reasonable to assume that it is the true mean facial WHR of CEOs. . Yes, since the suggested value of p would be a usual value to obtain in a sample of 51 CEQOs, itis reasonable to assume that it is the true mean facial WHR of CEOs. No, since the suggested value of p does not lie within the confidence interval from part a, it is not reasonable to assume that it is the true mean facial WHR of CEOs. Health care workers who use latex gloves with glove powder on a daily basis are particularly susceptible to developing a latex allergy. Each in a sample of 49 hospital employees who were diagnosed with a latex allergy based on a skin-prick test reported on their exposure to latex gloves. Summary statistics for the number of latex gloves used per week are x = 19.2 and s = 12.1. Complete parts (a) (d). a. Give a point estimate for the average number of latex gloves used per week by all health care workers with a latex allergy. b. Form a 95% confidence interval for the average number of latex gloves used per week by all health care workers with a latex allergy. (Use integers or decimals for any numbers in the expression. Round to two decimal places as needed.) c. Give a practical interpretation of the interval, part (b). () A. One can be 95% confident that the average number of latex gloves used per week by all healthcare workers with a latex allergy is greater than the upper boundary of the interval. . One can be 95% confident that the average number of latex gloves used per week by all healthcare workers with a latex allergy is in the interval. . One can be 95% confident that latex gloves cause allergies for all who use a number of gloves contained in the interval. . One can be 95% confident that the average number of latex gloves used per week by all healthcare workers with a latex allergy is less than the lower boundary of the interval. d. Give conditions required for the interval, part (b), to be valid. O A. i. The sample selected was randomly selected from the target population. ii. The sample size is sufficiently large, that is, n > 30 O B. i. The sample selected was randomly selected from the target population. ii. The sample size is sufficiently large, that is, n > 1000 O C. i. The sample selected was specifically selected from the target population. ii. The sample size is sufficiently large, that is, n > 1000 O D. i. The sample selected was specifically selected from the target population. ii. The sample size is sufficiently large, that is, n > 30Normal Curve Areas 0 N .00 .01 .02 03 .04 05 06 07 08 .0000 0040 .0080 .0120 .0160 .0199 0239 .0279 0319 .0398 .0438 .0478 .0517 .0557 .0596 .0636 .0675 0714 .0793 0832 .0871 .0910 0948 .0987 .1026 .1064 1103 .1179 .1217 .1255 .1293 1331 1368 .1406 .1443 .1480 .1554 .1591 .1628 .1664 .1700 .1736 .1772 .1808 .1844 .1915 .1950 .1985 .2019 .2054 .2088 2123 2157 .2190 .2257 2291 2324 2357 .2389 .2422 2454 .2486 .2517 2580 2611 .2642 .2673 .2704 .2734 .2764 .2794 2823 .2881 2910 .2939 .2967 2995 .3023 .3051 .3159 .3078 3186 .3106 .3212 .3238 .3264 .3289 .3315 .3340 .3365 1.0 .3413 3438 3461 .3485 .3508 3531 .3554 .3577 3599 1.1 .3643 3665 .3686 .3708 .3729 .3749 .3849 .3770 1.2 .3790 .3869 3810 3888 .3907 .3925 1.3 3944 .3962 .4032 3980 .3997 .4049 4066 4082 4099 1.4 4115 .4192 4131 4147 .4207 .4162 4222 4236 1.5 4251 4265 .4279 4292 4306 .4332 4345 4357 .4370 4382 4394 4406 4418 4429 1.6 .4452 .4463 .4474 .4484 4495 1.7 4505 .4515 .4554 4525 4535 .4564 4573 .4582 4591 4599 4608 1.8 4625 4641 .4616 .4649 .4656 .4664 .4671 1.9 .4678 4686 4693 .4713 4699 4719 4726 4732 4738 2.0 .4772 4744 4750 4756 .4778 4761 4783 .4788 4793 4798 .4803 .4808 4812 2.1 4821 4826 4830 .4834 4838 2.2 4842 .4846 4850 4854 .4861 4864 4868 2.3 4871 4875 4878 .4881 .4893 4884 4887 4896 4898 .4901 4904 2.4 4906 .4909 .4918 4920 4911 4913 4922 .4925 4927 2.5 4929 .4931 .4932 .4934 4938 .4940 4941 .4943 .4945 4946 4948 .4949 4951 2.6 4953 .4955 4956 .4957 .4959 2.7 4960 .4961 .4962 .4965 .4963 .4966 4967 .4968 2.8 4969 4970 .4971 .4974 4972 .4973 .4975 4976 4977 .4977 4978 .4979 4979 .4980 2.9 4981 .4982 4982 .4983 .4984 4984 .4985 4985 4986 3.0 .4987 4987 .4987 .4988 4988 .4989 .4989 4989 .4990 .00 .01 .02 .03 .04 .05 .06 .07 .08What is the confidence level of each of the following confidence intervals for p? Complete parts a through e. \fGreen Sea Turtle Curved Carapace Length Data 58.06 60.35 69.01 70.26 54.42 65.30 39.55 64.75 64.91 42.43 51.15 36.16 49.65 56.54 62.63 58.40 56.35 70.94 65.28 64.79 47.78 49.96 65.77 60.03 60.08 54.58 61.96 30.37 66.98 54.07 36.46 35.54 42.73 51.30 63.33 63.84 62.34 59.27 49.05 57.03 52.62 60.24 68.49 42.15 70.52 46.04 55.68 63.00 53.69 74.34 35.99 81.63 31.50 65.67 65.07 57.79 67.54 33.96 60.61 45.81 52.01 35.32 57.65 48.76 57.64 53.27 54.29 68.24 44.33 32.57 50.40 72.01 55.11 54.29The Aquatic Biology (Vol. 9, 2010) study collected data on green sea turtles inhabiting the Grand Cayman South Sound lagoon. The data on curved carapace (shell) length, measured in centimeters, for 74 captured turtles are displayed in the accompanying table. Environmentalists want to estimate the true mean shell length of all green sea turtles in the lagoon. Use these data to complete parts a through d. a. Define the parameter of interest to the environmentalists. The true mean shell length of green sea turtles in the sample The true mean shell length of all green sea turtles The true mean shell length of all turtles v The true mean shell length of green sea turtles in the lagoon b. Use the data to find a point estimate of the target parameter. A point estimate of the target parameter is 55.42 centimeters. (Round to two decimal places as needed.) c. Compute a 95% confidence interval for the target parameter. Interpret the result. (Round to two decimal places as needed.) O A. The 95% confidence interval indicates that 95% of values in the target population are between centimeters and centimeters. - The 95% confidence interval indicates that 95% of values in the sample are between centimeters and centimeters. . The 95% confidence interval indicates that the sample value of the target parameter is between centimeters and centimeters with 95% confidence. () D. The 95% confidence interval indicates that the true value of the target parameter is between centimeters and centimeters with 95% confidence