Figure 2. Child BMI by Group at Each Follow-up Time Point 30 Intervention Control 25 Observed Child Body Mass Index 20 15 10 3 9 12 24 36 Time, mo Which of the following statements best summarizes the body mass index (BMI) distributions for children randomized to the Intervention group compared to children randomized to the Control group over the 36-month study? a. While the medians for the two groups are similar at each of the times points, and generally consistent over time, the variation and number of outliers in the BMI distributions tend to increase over time. b. At the start of the study (time=0), most of the children (> 75%) randomized to the control group had BMIs larger in value than the median BMI for children randomized to the Intervention group. c. The two BMI distributions are heavily left-skewed at each of the featured time-points across the entire follow-up period. d. The difference in median BMI between the intervention and control groups consistently increases over the 36-month follow-up period.Restaurant Inspection Scores January 1- August 31, 2022 Austin, Texas US 12 Sample Summary Statistics (n=5,014) 10 Mean ( x ): 90.4 Standard Deviation (s): 8.0 Range: 44 to 100 Percentiles: 3rd : 72 Percentage of Restaurants 6 10th: 80 1 14: 81 50th: 92 75th:96 89 :99 90th :100 97th :100 Inspection Scores Maximum Score = 100) The standard deviation of the year 2022 inspection scores for these 5,014 restaurants is 8.0. Suppose you take a random sample of 200 of these 4,804 restaurants. How will the sample standard deviation ($200) of your 200 inspection scores compare in value to 8.0? a. S200 should be approximately equal to 8.0, but there is no way to predict exactly how S200 will compare in value to 8.0 b. S200 will definitely be smaller than 8.0. C. $200 will definitely be larger than 8.0. d. s200= (200/5,014) x 8.0 6. 1 pointInspection Scores by Year Restaurants in Austin TX USA = Inspection Score ................... .. .. ............ .. 2019 2020 * 2022 Scores For January through August You have recently been hired as the health commissioner for the city of Austin. You have received emails from 3 restaurant owners claiming the inspections have been made with inconsistent criteria for the years 2019 -2022. Is there evidence in these data of systematic inconsistency across the years? a. Yes, because the median score in 2019 was substantially lower than the median score in the other three years. b. Yes, because the restaurant scores are not (approximately) normally distributed in any of the years. c. No, because in each of the four years, some restaurants received perfect inspection scores of 100. d. No, because the distributions over the four years are generally similar in terms of shape, median values and the interquartile ranges (25th - 75th percentiles)