ANSWERS TO PRACTICE PROBLEMS FOR STAT 101 MIDTERM 1.This is longer than the actual midterm, but it gives you an idea of the types of questions that will be asked. Topics not covered in these problems still may be covered on exams.Name (Please print clearly) ________________________Lab Time (circle one): 8:30 – 9:45; 10:05 – 11:20; 11:40 – 12:55; 1:15 – 2:30Directions:1) Print clearly on this exam. Only correct solutions that can be read will be given credit.2) You may use a calculator and 1-page (with both sides) as crib sheets.3) Show your method of solution on problems requiring calculations. Only answers with supporting work will be given credit.4) Carry out all calculations to 2 decimal places of accuracy. You can leave answers in fractions.5) As a rough guideline, allot yourself about 9 minutes per page. If you get stuck, move on.The data for the problems on pages 2 – 5 of this exam pertain to a randomized experiment that assessed the effect of intensive childcare for children with low birth weights. The study is described on the next page.1Description of the study (READ THIS SO YOU KNOW WHAT THE STUDY IS ABOUT.)Low birth weight infants have elevated risks of cognitive impairment and academic failures later in life (Hill et al. 2003). One approach to reduce these risks is to provide extraordinary support for the families of low birth weight infants, for example intensive childcare education and access to trained specialists for the parents.To assess the effectiveness of such interventions, in 1985 researchers designed the Infant Health Development Program (IHDP). The IHDP involved randomizing 985 low birth weight infants to one of two groups: 1) a treated group assigned to receive weekly visits from specialists and to attend daily childcare at childhood development centers, and 2) a control group that did not have access to the weekly visits or childcare centers. There were 377 infants randomly assigned to the treated group and 608 randomly assigned to the control group. The outcome variable is the infant’s score on the Peabody Picture Vocabulary Test Revised administered at age 3. Infants took the test after completing the time period of the study.Questions begin here. For questions 1 – 17, circle the right answer. Below is a histogram of the Peabody test scores for the treated group.30 40 50 60 70 80 90 100 1201) The median score is closest to: 90 2) The SD is closest to: 15 3) The percentage of scores between 75 and 94.9 is closest to: 50% 4) The percentage of infants scoring 100 or higher is closest to: 25% 25) There are 54 treated infants whose Peabody scores are missing. Suppose through extra field work you obtain the 54 missing scores. You find that the mean and SD of these 54 scores are 93 and 4, respectively, and these 54 scores follow a normal curve. Which sentence best describes the SD for all 377 kids combined? b) The SD for the 377 is less than the SD from Question 2.3Below are box plots of the distributions of mothers’ age, Peabody scores, and birth weights in the treated and control groups: mom age203040Control TreatedtreatmentPeabody30405060708090100110120130Control Treatedtreatmentbirth w eight10002000Control Treatedtreatment6) We want our comparisons of the treated and control groups to be free of the effects of confounding variables. Which statement must be true for the comparisons to be free of confounding?b) The distributions of mothers’ age and birth weights should be similar in the treated and control groups. 7) True The treated and control groups have similar distributions of mothers’ age.8) The SD of the Peabody scores for the treated group is most likely (circle one of the following three choices) (i) about equal to the SD of the Peabody scores for the control group.9) What percentage of the control group was born weighing less than 2000 grams? 65% 10) Sketch a rough histogram of birth weights for the control group.should have a slight left skew11) Another variable measured in the study was the number of days the infant had to spend in the hospital after being born. The average of this variable for all 985 kids is 25.4 days and the SD is 23.9 days. Which of the following box plots looks most like the distribution of number of days spent in the hospital?b) box plot drawn with median less than 25.4 and long right tail..12) Consider the average days spent in the hospital for the treated and control groups. Which statement is most likely true?(ii) . The means in the treated and control groups are close to each other. This is because background characteristics are similarly 4distributed in control and treated groups in randomized experiments.Below are scatter plots of Peabody scores versus mothers’ age and versus birth weight for the control group. Shown in the plots involving are the regression lines.30405060708090100110120130Peabody15 20 25 30 35 40 45mom age30405060708090100110120130Peabody1000 2000birth w eight13) Estimate the slope and intercept of the regression line using mom age as the predictor. Slope around 0.7, intercept around 65.14) The correlation in the plot involving birth weights is closest to: 0 15) The correlation in the plot involving age is closest to: 0.20 16) If we measured mother’s age in terms of months and birth weight in terms of pounds, which statement is true:d) Neither correlation would change.517) A psychologist reads the article by Hill et al. (2003) and claims that the results are completely worthless, because the outcome variable is the score AFTER the treatment period ended rather than a change score (i.e., a post-study score minus a pre-study score). The psychologist says that there’s no way to tell if the childcare is more effective than the control because we cannot tell which group had the higher average increase in scores. Is the psychologist correct? Attack or defend the psychologist’s statement, using what youknow about the study design as described on page 2. Don’t just say “right” or “wrong”; explain why you think the psychologist is right or wrong. WRITE ONLY UP TO 4 SENTENCES. (THAT’S MORE THAN YOU NEED.)Not true. Because the study was randomized, the average “pre-intervention” scores in the control and treated groups should be similar. Hence, any difference in the sample post-intervention average scores should be attributable to the effect of the child