48. A Statistics 181/1P1 term test had 50 multiple-choice questions, each with four possible answers, only one ofwhich was correct. Suppose that one of the students who wrote the test answered each of the questions withan independent random guess. Determine an approximate probability that they answered at least 20 questionscorrectly if they could eliminate two wrong answers for each question and randomly chosen among the remaininganswers?(a) 0.9406.(b) 0.5881.(c) 0.1077.(d) 0.0594.49. The administrators for a hospital wished to estimate the average number of days required for treatment of patientsbetween the ages of 22 and 33. A random sample of 800 hospital patients between these ages produced a meanand standard deviation equal to 6.1 and 2.2 days, respectively. A 98% CI is given by [5.9191; 6.2808]. Interpretthis interval.(a) The true average number of days required for treatment of patients between the ages of 22 and 33 is in thisinterval with 98% confidence.(b) With a repeated random sampling of size 800, the true average number of days required for treatment ofpatients between the ages of 22 and 33 will be in this interval 98% of the time.(c) The sample mean = 6.1 is in this interval 98% of the time.(d) The true average number of days required for treatment of patients between the ages of 22 and 33 is in thisinterval with a probability of 98%.(Questions 50-52] A new drug is proposed to lower total cholesterol and a study is designed to evaluate its efficacy. Fifteenpatients were randomly selected to participate in the study and each is asked to take the new drug for 6 weeks. Beforestarting the treatment, each patient's total cholesterol level is measured. The initial measurement is a pre-treatment orbaseline value. After taking the drug for 6 weeks, each patient's total cholesterol level is measured again and the differencesbetween the values for subject (Baseline – 6 Weeks) are shown below.You may assume normality.Subject 1| 2 | 3| 4| 5| 6|7| 8 |9| 10 | 11 | 12 | 13 | 14 | 15d.|10 34 40 30 13 13 13 20 6 13|-12| -2| 36750. Which is the correct set of hypotheses for this study?(a) Ho : Ha = 0 vs H1 : Ha < 0.(b) Ho : 41 - µ2 = 0 vs H1 : H - #2 < 0.(c) Ho : H4 = 0 vs H1 : 44 >0.(d) Ho : d = 0 vs Hi :d< 0.51. Which is the correct rejection region at the 5% level of significance?(a) Taba> t13.0.025 = 2.160.(b) Tobs > t14.00.05 = 1.761.(c) Tubel >t40.025 = 2.145.(d) Tobe > t1a0.05 = 1.771.page 14 of 21Page Tatal:Version 40STA 1s1/1P1: September 2021page 15 of 2152. If the following table represents the Statistica output for this studyT-test for Dependent SamplesStd.DevMeanDiffStd.Devtp- valueConf.Conf.VariableDiff-95%+95%Baseline204.712.676-Weeks191.812.5912.9313.633.6750.00255.385220.4815Which statement is true?(a) Since the 95% confidence interval is ( 5.3852 , 20.4815 ) we can conclude there is no difference in thecholesterol levels between the baseline and the 6-weeks.(b) The 6-weeks cholesterol levels are in general higher than the baseline levels.(c) Since p - value = 0.0025 < a, we can conclude that the mean difference between the baseline and 6-weekscholesterol levels is insignificant.(d) Since the 95% confidence interval is ( 5.3852 , 20.4815 ) we can conclude there is a difference in thecholesterol levels between the baseline and the 6-weeks.53. Which of the following statements are true regarding the shape of distributions for quantitativedata?(a) When the mean, median and mode are equal then the data is skewed.(b) When the mean, median and mode are equal then the data is symmetrical.(c) When the mean is less than the mode then the data is positively skewed.(d) The shapes of distributions are determined by the mode only. 54. The probability is p = 0.40 that a patient with a certain disease will be unsuccessfully treated with a new medicaltreatment. Suppose that the expected value of the number of patients who are successfully treated is 39. Howmany patients was the treatment used on?(a) 65.(b) 97.5.(c) 15.6.(d) 98.55. For the hypotheses Ho : p = 0.2 vs H1 : p > 0.2, with an n = 100 and p = 0.24, what is the numerical value of theobserved value of the test statistic, that is the numerical value of Zob,?(a) 0.04.(b) 0.24.(с) 1.(d) 0.2.56. Suppose we are considering two populations with s = 4.43 and s2 = 5.93. Assume that the population variancesare equal and that n = ng. The pooled sample standard deviation is given by:(a) 5.18.(b) It cannot be determined because the sample sizes from each population must be specified.(c) 27.3949.(d) 5.2340.page 15 of 21Page Total:Version 40STA 1s1/1P1: September 2021page 16 of 257. If the critical value of a lower tailed test is z = -1.645, which is the correct numerical value of the confidencelevel?(a) 95%.(b) 97.5%.(c) 5%.(d) 90%.58. Suppose you wish to construct a 99% confidence interval for the mean when the population variance is unknown.You have a sample size of n = 300 and you make use of the t-table to determine the critical value. You go aheadand look up under degrees of freedom oo and probability 0.005 and find the critical value to be 2.576. Your friend inclass used the inverse normal table instead, under the area 0.995 and found the same answer as you for the criticalvalue. Was this just a coincidence or is there theory involved to explain why this is the case?(a) It was just a coincidence, there is no theory that exists to explain why the answers matched.(b) The answers were the same because there is no difference between the t-distribution and the normal distri-bution, the one implies the other.(c) The answers were the same because the t-distribution approximates the normal distribution for large samplesizes.(d) The answers were the same because the t-distribution and the normal distribution are both symmetricaldistributions.59. Achievement scores for a university entrance examination are normally distributed with a standard devia-tion of 1.314. If 97% of the scores are between 56.6083 and 62.3111, what is the mean for this distribu-tion?(a) 53.7569.(b) 59.4597.(e) -59.4597.(d) 58.5644.60. Suppose a random sample ofn pupils at Greenpoint Secondary School located in the Eastern Cape, were askedif they were in favour of having a one day on and one day off schedule for classes during the Covid 19 pandemic.A proportion of 75%, which translates to 375 pupils who were in favour of having a one day on and one day offschedule for classes during the Covid 19 pandemic. What was the sample size? At a 95% level of confidence, theerror margin is:(a) n = 500 and the error margin is 0.0380.(b) n = 375 and the error margin is 0.0438.(c) n = 500 and the error margin is 0.0319.(d) n = 375 and the error margin is 0.0224.61. Nearly a quarter of current South African university undergraduates are confident that doing an internship willhelp give them skills or knowledge to succeed in the job market and the workplace. This was the conclusion thatwas reached after a survey of 90 000 students at 26 randomly selected institutions in South Africa. Which of thefollowing is false?(a) Approximately a quarter is a statistic that was determined by the survey.(b) Approximately a quarter is a parameter that was determined by the survey.(c) The sample was the 90000 students who were surveyed.(d) The population was all undergraduate South African students at the various institutions.

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48. A Statistics 1si/1P1 term test had 50 multiple-choice questions, each with four possible answers, only one of which was correct. Suppose that one of the students who wrote the test answered each of the questions with an independent random guess. Determine an approximate probability that they answered at least 20 questions correctly if they could eliminate two wrong answers for each question and randomly chosen among the remaining answers? (a) 0.9406. (b) 0.5881. (c) 0.1077. (d) 0.0594.

48. A Statistics 1si/1P1 term test had 50 multiple-choice questions, each with four possible answers, only one of which was correct. Suppose that one of the students who wrote the test answered each of the questions with an independent random guess. Determine an approximate probability that they answered at least 20 questions correctly if they could eliminate two wrong answers for each question and randomly chosen among the remaining answers? (a) 0.9406. (b) 0.5881. (c) 0.1077. (d) 0.0594.

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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