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- A study was conducted to measure the effectiveness of hypnotism in reducing pain. The measurements are centimete on a pain scale before and after hypnosis. Assume that the paired sample data are simple random samples and that th differences have a distribution that is approximately normal. Construct a 95% confidence interval for the mean of the "before - after" differences. Does hypnotism appear to be effective in reducing pain? Before After 4.8 6.3 2.4 2.64. The following sample of numbers is chosen from a normally distributed population. 22, 25, 28, 30, 27 The 95% confidence interval for the population mean is (A) 26.4 + 1.0033 (B) 26.4 ± 1.3638 (C) 26.4 + 2.2435 (D) 26.4 + 2.6731 (E) 26.4 + 3.786033Calculate the mean and standard deviation of Height for the entire sample and for men and women separately and con-struct a 95% confidence interval around each of those means. ID Female Age Height Weight 6 0 25 65 200 18 0 27 66 155 77 1 21 63 135 80 0 22 68 130 84 0 22 68 184 100 1 22 66 127 119 0 28 71 155 150 0 26 66 110 157 1 23 63 150 184 1 24 65 120 219 1 26 65 110 227 1 28 63 135 232 0 24 69 150 270 0 23 68 150 285 1 24 61 137 297 1 28 62 175 349 0 27 66 180 383 0 25 68 140 446 1 27 61 97 448 0 21 68 150 454 1 24 68 125 462 1 25 69 150 479 0 22 73 145 505 0 26 71 195 556 0 28 72 215 573 0 24 72 155 585 1 22 61 110 596 0 23 68 150 646 1 23 61 128 682 1 22 68 140 689 1 21 65 106 691 1 24 63 143 698 1 26 69 120 706 1 28 61 103 717 0 23 74 215 722 0 27 73 236 763 0 23 69 155 774 0 25 66 123 795 0 22 71 178 810 1 25 60 105 834 1 26 62 167 850 0 24 68 150 890 0 26 73 180 939 1 27 66 130 971 1…A university wants to determine the population average grade of all students who take a statistics class online. The grade distribution of online statistics classes is normal. The average grade of 20 online statistics classes is 60% with a standard deviation of 15%. Find a 95% confidence interval for the average grade of all online statistics classes. (52.98, 67.02) (53.43, 66.57) (59.79, 60.21) O The sample size is too small to compute a confidence interval.If a certain machine manufactures electrical resistors that have a mean resistance of 40 ohms and a standard deviation of 2 ohms, what is the probability that a random sample of 36 of these resistors will have a combined resistance of more than 1458 ohms?Create a 90% confidence interval for the data set below. 53 62 62 58 60 61 70 53 70 59 61 60 ( , ) [three decimal accuracy] [three decimal accuracy]Twenty-one car salespeople were sampled to see how many cars they sold in a month; the following data was obtained:31, 28, 29, 29, 27, 24, 38, 30, 31, 27, 25, 35, 25, 30, 32, 30, 31, 29, 31, 23, 33Assuming the population standard deviation is σ=3, construct a 93% confidence interval for the mean number of cars sold per month by the population of car salespeople.xˉ=α2=zα2=Margin of Error: E=We are 93% confident that, on average, car salespeople sell between cars and cars per month.a simple random sample of 9 college freshmen were asked how many hour of sleep they typically got per night. The results were 8.5,6.5,8,9,6,7.5,24,8.5,9.5. Elminate the outlier, then consturct a 90% confidence interval for the mean amount of sleep from the remaining values.Create a 95% confidence interval for the data set below. 70 59 58 72 66 58 70 70 64 59 56 68 72 68 ( , ) [three decimal accuracy] [three decimal accuracy]9. A random sample of 25 statistics examinations was taken. The average score in the sample was 76 with a variance of 144. Assuming the scores are normally distributed, the 99% confidence interval for the population average examination score is a. 70.02 to 81.98 b. 69.82 to 82.18 C. 70.06 to 81.94 d. 69.48 to 82.52Find the 98% confidence interval for the difference between two means based on this information about two samples. Assume independent samples from normal populations. (Use conservative degrees of freedom.) (Give your answers correct to two decimal places.) Sample Number Mean Std. 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